Calculus Help
saxi753
- 32 / 200
1
We have not discussed methods by which systems of first-order differential equations can be solved
18:46

We have not discussed methods by which systems of first-order differential equations can be solved

We have not discussed methods by which systems of first-order differential equations can be solved. Nevertheless, systems such as (2) can be solved with no knowledge other than how to solve a single linear first-order equation. Find a solution of (2) subject to the initial conditions x(0)= x_0, y(0)=0, z(0)=0. dx/dt=-λ_1 x dy/dt=λ_1 x-λ_2 y dz/dt=λ_2 y #DifferentialEquations #Calculus #Techniques #SystemOfEquations
2
Differential Equations: Potassium-40 Decay: The chemical element potassium is a soft metal that can
15:17

Differential Equations: Potassium-40 Decay: The chemical element potassium is a soft metal that can

Potassium-40 Decay The chemical element potassium is a soft metal that can be found extensively throughout the Earth's crust and oceans. Although potassium occurs naturally in the form of three isotopes, only the isotope potassium-40 (K-40) is radioactive. This isotope is also unusual in that it decays by two different nuclear reactions. Over time, by emitting beta particles a great percentage of an initial amount K₀ of K-40 decays into the stable isotope calcium-40 (Ca-40), whereas by electron capture a smaller percentage of K₀ decays into the stable isotope argon-40 (Ar-40). Because the rates at which the amounts C(t) of Ca-40 and A(t) of Ar-40 increase are proportional to the amount K(t) of potassium present, and the rate at which K(t) decays is also proportional to K(t), we obtain the system of linear first-order equations dC/dt=λ_1 K dA/dt=λ_2 K dK/dt=-(λ_1+λ_2)K where λ₁ and λ₂ are positive constants of proportionality. By proceeding as in Problem 1, we can solve the mathematical model described. (a) From the last equation in the given system of differential equations, find K(t) if K(0) = K₀. Then use K(t) to find C(t) and A(t) from the first and second equations. Assume that C(0) = 0 and A(0) = 0. (b) It is known that λ₁ = 4.7526 × 10⁻¹⁰ and λ₂ = 0.5874 × 10⁻¹⁰. Find the half-life of K-40. (c) Use C(t) and A(t) found in part (a) to determine the percentage of an initial amount K₀ of K-40 that decays into Ca-40 and the percentage that decays into Ar-40 over a very long period of time. #CalculusHelp #DiffernetialEquations #SystemOfEquations
3
Calculus Help: Differential Equations: The sine integral function x^3 dy/dx+2x^2 y=10sinx, y(1)=0
5:16

Calculus Help: Differential Equations: The sine integral function x^3 dy/dx+2x^2 y=10sinx, y(1)=0

The sine integral function is defined as Si(x)=∫_0^x sint/t dt Where the integrand is defined to be 1 at x = 0. Express the solution of the initial-value problem x^3 dy/dx+2x^2 y=10sinx ,y(1)=0 In terms of Si(x) #DifferentialEquations #SineIntegral #Calculus #Techniques
4
Calculus Help: Find an explicit solution of the given initial-value problem dy/dx=ye^(-x^2 ),y(4)=1
3:25

Calculus Help: Find an explicit solution of the given initial-value problem dy/dx=ye^(-x^2 ),y(4)=1

Calculus Help: Find an explicit solution of the given initial-value problem dy/dx=ye^(-x^2 ),y(4)=1 #CalculusHelp #DummyVariable #DifferentialEquations
5
Calculus: Linear Ordinary Differential Equation: L di/dt+Ri=E,i(0)=i_0 ,L,R,E,i_0 constants
6:03

Calculus: Linear Ordinary Differential Equation: L di/dt+Ri=E,i(0)=i_0 ,L,R,E,i_0 constants

Calculus: Linear Ordinary Differential Equation: L di/dt+Ri=E,i(0)=i_0 ,L,R,E,i_0 constants #DifferentialEquations #LinearODE #CalculusHelp
6
Calculus Help: Find the solution of differential equation dy/dx+2y=f(x),y(0)=0, f(x)={ (1,0≤x≤3@0,
11:02

Calculus Help: Find the solution of differential equation dy/dx+2y=f(x),y(0)=0, f(x)={ (1,0≤x≤3@0,

Find the solution of differential equation dy/dx+2y=f(x),y(0)=0,where f(x)={ (1,0≤x≤3@0, x≫3) #DifferentialEquations #PiecewiseFunctions #Calculus
7
Calculus Help: Use Euler’s method to approximate the solution to the given initial value problem
9:17

Calculus Help: Use Euler’s method to approximate the solution to the given initial value problem

Use Euler’s method to approximate the solution to the given initial value problem at the points x = 0.1, 0.2, 0.3, 0.4, and 0.5, using steps of size 0.1 (h = 0.1). dy/dx=x+y,y(0)=1,h=0.1 #EulerMethod #Approximation
8
Calculus Help: Determine whether the given set of functions is linearly independent on the interval
6:35

Calculus Help: Determine whether the given set of functions is linearly independent on the interval

Determine whether the given set of functions is linearly independent on the interval (-∞,∞) f1 (x)=1+x, f2 (x)=x , f3 (x)=x^2 #LinearlyIndependent #LinearlyDependent #CalculusHelp #WronskianMatrix #Matrix
9
Calculus Help: Determine whether the given set of functions is linearly independent on the interval
8:01

Calculus Help: Determine whether the given set of functions is linearly independent on the interval

Calculus Help: Determine whether the given set of functions is linearly independent on the interval Determine whether the given set of functions is linearly independent on the interval (-∞,∞) f_1 (x)=x, f_2 (x)=x^2 , f_3 (x)=4x- 3x^2 #LinearlyDependent #linearlyindependent #CalculusHelp
10
Calculus Help: Differential Equations - Linear ODE - Integrating Factor - y'=sinx (y secx-2)
4:29

Calculus Help: Differential Equations - Linear ODE - Integrating Factor - y'=sinx (y secx-2)

Calculus Help: Differential Equations - Linear ODE - Integrating Factor - y'=sinx (y secx-2) #DifferentialEquations #LinearODE #ODE #CalculusHelp
11
Calculus Help: Differential Equations - Exact - y'=(2y^2-3x^3)/(1-4xy) - Techniques
5:13

Calculus Help: Differential Equations - Exact - y'=(2y^2-3x^3)/(1-4xy) - Techniques

Calculus Help: Differential Equations - Exact - y'=(2y^2-3x^3)/(1-4xy) - Techniques #DifferentialEquations #Exact #CalculusHelp #Techniques
12
Calculus Help: Differential Equations - Homogeneous - x y^4 dy+(5x^5-2y^5 ) dx=0
6:37

Calculus Help: Differential Equations - Homogeneous - x y^4 dy+(5x^5-2y^5 ) dx=0

Calculus Help: Differential Equations - Homogeneous - x y^4 dy+(5x^5-2y^5 ) dx=0 #DifferentialEquations #CalculusHelp #Homogeneous
13
The population density of a certain city is given by p(x,y) = 4x^2 + 5y, where x and y are
10:11

The population density of a certain city is given by p(x,y) = 4x^2 + 5y, where x and y are

The population density of a certain city is given by p(x,y) = 4x + 5y, where x and y are in miles and p is the number of people per square mile, in hundreds. The city limits are as shown in the accompanying graph. a) Determine the city's population. b) Determine the average number of people per square mile of the city.
14
Multivariable Limits: lim (xy-10x^2 y)/4xy , lim (√(x+y)-4)/(x+y-16) , lim (√(y+3)-√x)/(y+3-x)
3:54

Multivariable Limits: lim (xy-10x^2 y)/4xy , lim (√(x+y)-4)/(x+y-16) , lim (√(y+3)-√x)/(y+3-x)

lim((x,y)→(0,0))⁡ (xy-10x^2 y)/4xy lim((x,y)→(5,11))⁡ (√(x+y)-4)/(x+y-16) lim((x,y)→(7,4))⁡ (√(y+3)-√x)/(y+3-x) #MultivariableLimits #Limits #Calculus #Variables
15
Calculus Help: Homogeneous Differential Equations: (x-4y)dx+(x+2y)dy=0,y=1,x=1
10:14

Calculus Help: Homogeneous Differential Equations: (x-4y)dx+(x+2y)dy=0,y=1,x=1

Calculus Help: Homogeneous Differential Equations: (x-4y)dx+(x+2y)dy=0,y=1,x=1 #Homogeneous #DifferenitalEquations #Calculus
16
Differential Equation Integrating Factor by Inspection: (x^2 y + y^3- y)dx + (x^3+xy^2+x)dy=0
2:31

Differential Equation Integrating Factor by Inspection: (x^2 y + y^3- y)dx + (x^3+xy^2+x)dy=0

Differential Equation Integrating Factor by Inspection: (x^2 y + y^3- y)dx + (x^3+xy^2+x)dy=0 #DifferentialEquations #Inspection #Calculus
17
Calculus Differential Equations - Integrating Factor by Inspection: (x^3+xy^2-y)dx+(y^3+x^2 y+x)dy=0
5:27

Calculus Differential Equations - Integrating Factor by Inspection: (x^3+xy^2-y)dx+(y^3+x^2 y+x)dy=0

Calculus Differential Equations - Integrating Factor by Inspection: (x^3+xy^2-y)dx+(y^3+x^2 y+x)dy=0 Calculus Differential Equations - Integrating Factor by Inspection: (x^3+xy^2-y)dx+(y^3+x^2 y+x)dy=0 #Calculus #DifferentialEquations #Inspection #Technqiues
18
Calculus Help: Separable Differential Equations - y^2 (y^2+1)dx+x (y^2-1) dy=0
3:30

Calculus Help: Separable Differential Equations - y^2 (y^2+1)dx+x (y^2-1) dy=0

Here is the technique to solve this differential equation and how to find them in step-by-step Calculus Help: Separable Differential Equations - y^2 (y^2+1)dx+x (y^2-1) dy=0 #SeparableDifferentialEquations #DifferentialEuqations
19
Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals
2:45

Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals

Calculus Help: ∫ (20x^3)/(1+x^4 )^4 dx - Integration by substitution #Substitution #Integrals #Antiderivative #Calculus
20
Calculus Help: Find the limits - lim (x→1)⁡ (x^2-1)/(√x-1 ) - Techniques
1:50

Calculus Help: Find the limits - lim (x→1)⁡ (x^2-1)/(√x-1 ) - Techniques

Calculus Help: Find the limits - lim (x→1)⁡ (x^2-1)/(√x-1 ) - Techniques #Limits #Calculus #Techniques
21
Calculus Help: Separable Differential equations - y=2xy'-2y'+1 - Techniques
1:41

Calculus Help: Separable Differential equations - y=2xy'-2y'+1 - Techniques

Separable Differential equations - y=2xy'-2y'+1 - Techniques #separabledifferentialequations #differentialequation
22
Calculus Help: Bernoulli's Equations - dy/dx-4y=2xy^2 ,y(0)=-4
7:03

Calculus Help: Bernoulli's Equations - dy/dx-4y=2xy^2 ,y(0)=-4

Calculus Help: Bernoulli's Equations - dy/dx-4y=2xy^2 ,y(0)=-4 #BernoulliEquations #Equations #CalculusHelp
23
Calculus Help: Separable Differential Equations: (e^t y+t e^t y) dt+(t e^t+2)dy=0 ,y(0)=-1
3:23

Calculus Help: Separable Differential Equations: (e^t y+t e^t y) dt+(t e^t+2)dy=0 ,y(0)=-1

(e^t y+t e^t y) dt+(t e^t+2)dy=0 ,y(0)=-1 #SeparableDifferentialEquations #DifferentialEquations #CalculusHelp #Techniques
24
Calculus Help: How to compute double summation ∑∑ (i - j) - Basic - Step-by-step
2:38

Calculus Help: How to compute double summation ∑∑ (i - j) - Basic - Step-by-step

Calculus Help: How to compute double summation ∑∑ (i - j) - Basic - Step-by-step #DoubleSummation #Summation #Calculus
25
The graph above shows the base of an object. Compute the exact value of the
5:10

The graph above shows the base of an object. Compute the exact value of the

The graph above shows the base of an object. Compute the exact value of the volume of the object, given that cross sections (perpendicular to the base) are squares. #CrossSection #Area #Volume #Integrals
26
Calculus Help: A ball of radius 13 has a round hole of radius 9 drilled through its center.
9:15

Calculus Help: A ball of radius 13 has a round hole of radius 9 drilled through its center.

A ball of radius 13 has a round hole of radius 9 drilled through its center. #Radius #Calculus #Integral #Volume #Integrations
27
Calculus Help: Find 4∑ (5i)i=1 First write out the summation: Find the answer
0:55

Calculus Help: Find 4∑ (5i)i=1 First write out the summation: Find the answer

Calculus Help: Find 4∑ (5i)i=1 First write out the summation: Find the answer #Summation #Calculus
28
Calculus Help: Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts
1:56

Calculus Help: Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts

Calculus Help: If I_n=∫ x^n e^x dx ,n∈NProve that I_n=x^n e^x-nI_(n-1) #Parts #Integrals #Techniques
29
Calculus Help: Reverse the order with the order of integration and evaluate ∫ ∫ cos(32π x^6) dx dy
11:13

Calculus Help: Reverse the order with the order of integration and evaluate ∫ ∫ cos(32π x^6) dx dy

#DoubleIntegrals #Integrations #Reversed #Calculus
30
Calculus Help: Find the limit: lim (x→0)⁡ sin^2⁡ (3x) /(1-cos2x) - Techniques
2:08

Calculus Help: Find the limit: lim (x→0)⁡ sin^2⁡ (3x) /(1-cos2x) - Techniques

Calculus Help: Find the limit: lim (x→0)⁡ sin^2⁡ (3x) /(1-cos2x) - Techniques #Calculus #Limit #Functions
31
Calculus Help: Separable Differential Equations: √(4+x^2 ) y^'-xy^2=0 ,y(0)=-1/4
4:53

Calculus Help: Separable Differential Equations: √(4+x^2 ) y^'-xy^2=0 ,y(0)=-1/4

Calculus Help: Separable Differential Equations: √(4+x^2 ) y^'-xy^2=0 ,y(0)=-1/4 #SeparableDifferentialEquations #DifferentialEquations
Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a
19:49

Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a

An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water resistance. (a) (4 points) If the water resistance is proportional to the object's velocity v(t) with coefficient b ≫ 0, so that Newton's second law gives b dv/dt =g- b/m v show that the object's velocity as a function of time t is given by v(t) = mg/b (1-e^(-bt/m)). We take downward to be the positive direction and the object is at rest when it is dropped at t=0. (b) (4 points) If instead the water resistance is quadratic in the velocity, so that Newton's second law gives dv/dt =g- b/m v^2 dt m dv dt find the object's velocity as a function of time t, again assuming that the object is dropped from rest. [Hint: Write Newtons' law as = g(1 − k^2v^2) where k = √b/mg. Then the algebra is a little less messy. After obtaining the final answer in terms of k, remember to replace k by √b/mg.] (c) (2 points) If the object could fall forever under these conditions without hitting the bottom, show that as t→ ∞ the velocity in part (a) approaches terminal velocity v → mg/b. What terminal velocity does the velocity in part (b) approach? #CalculusHelp #Integrals #differentialequations #PartialFractions
33
Calculus : Multivariable Limit - lim((x,y)→(0,0))⁡ (x^4+y^4)/(x^3-y^3 ) - Techniques
1:50

Calculus : Multivariable Limit - lim((x,y)→(0,0))⁡ (x^4+y^4)/(x^3-y^3 ) - Techniques

Calculus Help: Multivariable Limit - lim((x,y)→(0,0))⁡ (x^4+y^4)/(x^3-y^3 ) - Techniques #MultivariableLimit #Limits #Calculus
34
Calculus Inverse Laplace Transformation L^(-1) {1/(1+s^2 )^2 } - Techniques
1:23

Calculus Inverse Laplace Transformation L^(-1) {1/(1+s^2 )^2 } - Techniques

Inverse Laplace Transformation L^(-1) {1/(1+s^2 )^2 } #InverseLaplaceTransformation #LaplaceTransformation #Calculus
35
Integral: ∫ cosx cos^2⁡ (sinx)dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx)dx ∫sinx sin^2⁡(cosx)dx
5:38

Integral: ∫ cosx cos^2⁡ (sinx)dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx)dx ∫sinx sin^2⁡(cosx)dx

Here is the technique to solve these 4 integrals by integration by substitution ∫ cosx cos^2⁡ (sinx) dx ∫ sinx cos^2⁡ (cosx) dx ∫ cosx sin^2⁡ (sinx) dx ∫ sinx sin^2⁡ (cosx) dx #CalculusHelp #Integral #Integrations #IntegrationbySubstitution #Substitution
36
Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques
4:55

Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques

Calculus Help: Integral ∫ sin2x/e^x dx - Integration by parts - Techniques #Integral #Integrations #Calculus #Formula #Parts
37
Calculus Help: Euler's Method Approximation: Given initial value: x=0.1,0.2,0.3 dy/dx=y(6-y), y(0)=4
3:48

Calculus Help: Euler's Method Approximation: Given initial value: x=0.1,0.2,0.3 dy/dx=y(6-y), y(0)=4

Calculus Help: Euler's Method Approximation: Given initial value: x=0.1,0.2,0.3 dy/dx=y(6-y), y(0)=4 #Euler #Approximation #Calculus
38
Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution
5:38

Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution

Calculus Help: Integral ∫ 1/(3+2tanx) dx - Find the coefficient - Integration by substitution #Integral #Integrations #Calculus #Antiderivative
39
Second-order homogeneous linear difference equation with constant coefficients - Recurrence relation
8:02

Second-order homogeneous linear difference equation with constant coefficients - Recurrence relation

Second-order homogeneous linear difference equation with constant coefficients - Recurrence relation #Calculus #Techniques
40
Calculus: First-order Linear Difference Equations with Constant Coefficient - recurrence relations
3:15

Calculus: First-order Linear Difference Equations with Constant Coefficient - recurrence relations

Calculus: First-order Linear Difference Equations with Constant Coefficient - recurrence relations #Calculus #Techniques
41
Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution
1:46

Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution

Calculus Help: Integral ∫ (x+1) e^2x e^(x^2 ) dx - Integration by substitution #Calculus #Integral #Integrations #Substitution
42
Calculus Help: Integral ∫ ∛(e^arccot⁡(4x) )/(16x^2+1) dx - Integration by substitution
2:37

Calculus Help: Integral ∫ ∛(e^arccot⁡(4x) )/(16x^2+1) dx - Integration by substitution

∫▒〖∛(e^arccot⁡(4x) )/(16x^2+1) dx〗 Integration by substitution #Integration #Calculus #Substitution #Techniques
43
Calculus Help: ∫ (2+(lnx)^2)/(x(2-lnx)) dx - Integration by substitution
3:25

Calculus Help: ∫ (2+(lnx)^2)/(x(2-lnx)) dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Substitution
44
Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division
3:01

Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division

Calculus Help: Integral of ∫ arctanx / x^2 dx - Integration by parts and division #Integral #Calculus #Parts
45
Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution
2:51

Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ 1/(x^3+x) dx - Integration by trigonometric substitution #Integral #Integrations #Calculus #Techniques #TrigonometricSubstitution
46
Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution
2:13

Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution

Calculus Help: Integral ∫ dx/(x^2 √(x^2-1)) - Integration by trigonometric substitution #Integral #Integrations #Trigonometric #Techniques
47
Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution
3:44

Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution

Calculus Help: Integral of dx/(x^3 √(x^2-1)) - Integration of trigonometric substitution #Integral #Substitution #Trigonometric
48
Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution
6:19

Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ x^3/√(x^2+100) dx - Integration by trigonometric substitution #Integral #Trigonometric #Substitution #Calculus
49
Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution
3:26

Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution

Calculus Help: Integral ∫ dx/(x^2 √(x^2-9)) - Integration by trigonometric substitution #Trigonometric #Substitution #Integrals #Calculus
50
Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution
9:20

Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution

Calculus Help: Integral from 0 to 1 x^x dx - Gamma Function - Taylor Series - Substitution Here is the technique to solve this question and how to find them in step-by-step #Techniques #Solutions #Answers #Formula #GammaFunctions #Substitution
51
Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED!
4:45

Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED!

Calculus Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Techniques - SOLVED! #TrigonometricSubstitution #Substitution #Calculus
52
In 2004, an art collector paid $72719000 for a particular painting. The same painting sold for
7:09

In 2004, an art collector paid $72719000 for a particular painting. The same painting sold for

In 2004, an art collector paid $72719000 for a particular painting. The same painting sold for $34000 in 1950. a) Find the exponential growth rate k, three decimal places, and determine the exponential growth function V, for which V(t) is the painting's value, in dollars, t years after 1950 b) Predict the value of the painting in 2026 c) Estimate the rate of change of the painting's value in 2026 d) How long after 1950 will the value of the painting be $4 billion #ExponentialFunction #Exponential #Calculus
53
Calculus Help: Separable Differential Equations - (1+y^2 )dx+(1+x^2 )dy=0
1:11

Calculus Help: Separable Differential Equations - (1+y^2 )dx+(1+x^2 )dy=0

Calculus Help: Separable Differential Equations - (1+y^2 )dx+(1+x^2 )dy=0 #DifferentialEquations #Calculus #Separable #Techniques #CalculusHelp
54
Calculus Help: Integral ∫ x sin⁡(x/a)dx - Integration by parts - Techniques
2:54

Calculus Help: Integral ∫ x sin⁡(x/a)dx - Integration by parts - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Parts #Calculus
55
Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts
2:07

Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts

Calculus Help: Find the value of integral of x^2 lnx dx - Integration by parts #Integral #Integration #Calculus #Parts
56
Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques
1:19

Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques

Calculus Help: Improper Integrals - ∫ From 1 to ∞ 1/x^2 dx - Integration - Techniques #ImproperIntegrals #Integrations #Calculus #Integral #Antiderivative
57
Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques
3:02

Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques

Calculus Help: Integral ∫ (x^2-3x)/√(x+4) dx - Integration by substitution - Techniques #Integrals #Integrations #Calculus #Antiderivative
58
Calculus Help: How to determine One-to-one function by illustration
4:33

Calculus Help: How to determine One-to-one function by illustration

Calculus Help: How to determine One-to-one function by illustration #OneToOne #Functions #Calculus #Algebra
59
Calculus Help: Reverse the inverse function: f^(-1) (x) = 2x^3 + 3, write the original function f(x)
1:35

Calculus Help: Reverse the inverse function: f^(-1) (x) = 2x^3 + 3, write the original function f(x)

Calculus Help: Reverse the inverse function: f^(-1) (x) = 2x^3 + 3, write the original function f(x) #InverseFunctions #Functions #Calculus
60
Calculus Help: Find the inverse functions - y=2x/(x-3) - Techniques
1:26

Calculus Help: Find the inverse functions - y=2x/(x-3) - Techniques

Calculus Help: Find the inverse functions - y=2x/(x-3) - Techniques #Techniques #Calculus
61
Find the domain of the function: √(x-1)/(x-5) ,3x/√(x+4) ,x/(x^2-9)
5:59

Find the domain of the function: √(x-1)/(x-5) ,3x/√(x+4) ,x/(x^2-9)

Find the domain of the function: √(x-1)/(x-5) ,3x/√(x+4) ,x/(x^2-9) #Domain #Functions #Calculus #Formula
62
Calculus Help: Find the domain of function y=x^2/(x-1) y= √(x^2-5x+6) - Techniques
1:47

Calculus Help: Find the domain of function y=x^2/(x-1) y= √(x^2-5x+6) - Techniques

Calculus Help: Find the domain of function y=x^2/(x-1) y= √(x^2-5x+6) - Techniques #Domain #Calculus #Functions
63
Calculus Help: How to find the domain and the range of inverse function by f(x) graph?
2:34

Calculus Help: How to find the domain and the range of inverse function by f(x) graph?

Calculus Help: How to find the domain and the range of inverse function by f(x) graph? #Domain #Range #InverseFunctions #Calculus
64
Calculus Help: Find domain: f(x)=(x-3)/(x^2-3x-4); g(x)=4-√(x+9), h(x)=√((x-6)/(x+1)) , f(u)=√(u+1)
4:19

Calculus Help: Find domain: f(x)=(x-3)/(x^2-3x-4); g(x)=4-√(x+9), h(x)=√((x-6)/(x+1)) , f(u)=√(u+1)

Calculus Help: Find domain: f(x)=(x-3)/(x^2-3x-4); g(x)=4-√(x+9), h(x)=√((x-6)/(x+1)) , f(u)=√(u+1) #Domain #Calculus #Techniques
65
Piecewise Function: How to graph the function step-by-step? (Basic)
6:55

Piecewise Function: How to graph the function step-by-step? (Basic)

Piecewise function f(x): x+2 , x ≤ -1; x^2 , x > -1 f(x): x^2 , x ≥ 1 , √x , 0 ≤ x < 1 #StepbyStep #PiecewiseFunction #Calculus
66
Calculus Help: Find the inverse function, range and domain :y=ln⁡((x-1)/(x+1))
4:47

Calculus Help: Find the inverse function, range and domain :y=ln⁡((x-1)/(x+1))

Calculus Help: Find the inverse function, range and domain :y=ln⁡((x-1)/(x+1)) #InverseFunction #Domain #Range
67
Evaluate ∭_E z dV where E lies above the paraboloid z=x^2+y^2 and below the plane z=2y
12:59

Evaluate ∭_E z dV where E lies above the paraboloid z=x^2+y^2 and below the plane z=2y

Evaluate ∭_E z dV where E lies above the paraboloid z=x^2+y^2 and below the plane z=2y #PolarCoordinates #Techniuqes #Evaluate #TripleIntegrals
68
Bernoulli Differential Equations: y'+xy=xy^2 , x^2 y'+2xy=y^4 , y'+y=y^4 , y'+1/x y=1/y - SOLVED!!!
15:45

Bernoulli Differential Equations: y'+xy=xy^2 , x^2 y'+2xy=y^4 , y'+y=y^4 , y'+1/x y=1/y - SOLVED!!!

Bernoulli Differential Equations: y'+xy=xy^2 , x^2 y'+2xy=y^4 , y'+y=y^4 , y'+1/x y=1/y - SOLVED!!! #Bernoulli #BernoulliDifferentialEquations #DifferentialEquations #Calculus #Techniques
69
Calculus Help: Bernoulli's Equations - x^3 y'+x^2 y=2y^(-4/3) - Techniques - SOLVED!!!
6:50

Calculus Help: Bernoulli's Equations - x^3 y'+x^2 y=2y^(-4/3) - Techniques - SOLVED!!!

Calculus Help: Bernoulli's Equations - x^3 y'+x^2 y=2y^(-4/3) - Techniques - SOLVED!!! #Bernoulli #BernoulliEquation #DifferentialEquations
70
Calculus Help: Bernoulli's Differential Equations - x^2 y'+2xy=5y^3 - Techniques
5:32

Calculus Help: Bernoulli's Differential Equations - x^2 y'+2xy=5y^3 - Techniques

x^2 y'+2xy=5y^3 Bernoulli' s Equation #BernoulliEquation #Bernoulli #DifferentialEquations #LinearODE
71
Laplace Transformation - System of Differential Equations: dx/dt+x-2y=0, dy/dt+x+4y=0, x(0)=1,y(0)=1
11:47

Laplace Transformation - System of Differential Equations: dx/dt+x-2y=0, dy/dt+x+4y=0, x(0)=1,y(0)=1

Laplace Transformation - System of Differential Equations: dx/dt+x-2y=0, dy/dt+x+4y=0, x(0)=1,y(0)=1 #LaplaceTransformation #DifferentialEquations #Calculus #Techniques #ToanCaoCap #ToanGiaiTich
72
Laplace Transformation-f(t)=3t^3-5t^2+6, f(t)=6e^5t-5t, f(t)=cos⁡(3t)+3e^2t, f(t)=3cos⁡(2t)-sin⁡(4t)
3:20

Laplace Transformation-f(t)=3t^3-5t^2+6, f(t)=6e^5t-5t, f(t)=cos⁡(3t)+3e^2t, f(t)=3cos⁡(2t)-sin⁡(4t)

Laplace Transformation-f(t)=3t^3-5t^2+6, f(t)=6e^5t-5t, f(t)=cos⁡(3t)+3e^2t, f(t)=3cos⁡(2t)-sin⁡(4t) #LaplaceTransformation #ToanCaoCap #ToanGiaiTich
73
Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution
1:50

Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution

Calculus Help: Integral of ∫ dx/√(25-x^2 ) - Integration by trigonometric substitution #Integral #TrigonometricSubstitution #Calculus
74
y''-4y^'+4y=7sinx-cosx - Complementary Solutions and Particular Solutions - Differential Equations
10:01

y''-4y^'+4y=7sinx-cosx - Complementary Solutions and Particular Solutions - Differential Equations

y''-4y^'+4y=7sinx-cosx - Complementary Solutions and Particular Solutions - Differential Equations #DifferentialEquations #Calculus #Techniques #Solutions #ComplementarySolutions #ParticularSolutions
75
Calculus Help: Differential Equations - Linear ODE - y'+x/(x^2+1) y=x - Step-by-step
5:50

Calculus Help: Differential Equations - Linear ODE - y'+x/(x^2+1) y=x - Step-by-step

Here is the technique to solve this question and how to find them in step-by-step #Integral #DifferentialEquations #Calculus
76
Calculus Help: Differential Equations - Homogeneous - y'=(y+2√xy)/x ,x>0,y(1)=1
6:29

Calculus Help: Differential Equations - Homogeneous - y'=(y+2√xy)/x ,x>0,y(1)=1

Here is the technique to solve this differential equations and how to find them in step-by-step #DifferentialEquations #Calculus #Formula #Homogeneous
77
Calculus Help: Find the limits - lim (x→3)⁡ (x^3-27)/(x-3) - Techniques - SOLVED!!!
1:24

Calculus Help: Find the limits - lim (x→3)⁡ (x^3-27)/(x-3) - Techniques - SOLVED!!!

Calculus Help: Find the limits - lim (x→3)⁡ (x^3-27)/(x-3) - Techniques - SOLVED!!! #Limit #Functions #Calculus
78
Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions
1:25

Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions

Calculus Help: Integral: x e^(x^2) dx - Integration by substitution - Techniques - Solutions #Integration #Calculus #Substitution
79
Calculus Help: Integral of e^(x^2) - Imaginary Error Function
1:10

Calculus Help: Integral of e^(x^2) - Imaginary Error Function

Calculus Help: Integral of e^(x^2) - Imaginary Error Function #Integral #ImaginaryErrorFunction #Calculus
80
Calculus Help: Determine the area under the curve y^2=4x and y-2x+4=0 - Application of Integration
6:14

Calculus Help: Determine the area under the curve y^2=4x and y-2x+4=0 - Application of Integration

Here is the technique to solve this integration and how to find them in here #Integral #Integration #Calculus #Formula #Techniques #Answers
81
Calculus Help: Integral ∫ From 0 to 1 sinx tanx dx - Basic Trigonometry
3:09

Calculus Help: Integral ∫ From 0 to 1 sinx tanx dx - Basic Trigonometry

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
82
Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution
4:09

Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution

Calculus Help: Integral of 1/(x^2 √(9-x^2 )) dx - Integration by Trigonometric Substitution #Integration #Integrals #Trigonometric #Substitution #Calculus
83
Calculus Help: ∫_0^1 arcsinx dx Integration by parts and substitution
5:12

Calculus Help: ∫_0^1 arcsinx dx Integration by parts and substitution

Here is the technique to solve this integration and how to find it ∫_0^1▒arcsinx dx Integration by parts #Integral #Integrations #Calculus #Substitution
84
Calculus Help: Integral ∫ 0^2 x√(3x^2+5) dx - Integration by substitution
3:54

Calculus Help: Integral ∫ 0^2 x√(3x^2+5) dx - Integration by substitution

Here is the technique to solve this question and how to find them in step-by-step #Calculus #Integral #Integrations
85
Calculus Help: Find the limits - lim(x→2)⁡ (4-2x)/(4-x^2 ) - Techniques - SOLVED!!
0:57

Calculus Help: Find the limits - lim(x→2)⁡ (4-2x)/(4-x^2 ) - Techniques - SOLVED!!

Calculus Help: Find the limits - lim(x→2)⁡ (4-2x)/(4-x^2 ) - Techniques - SOLVED!! #Limits #CalculusHelp
86
Complementary and Particular: y''-4y'+4y=2+8x-4x^2- Undetermined Coefficients -Differential Equation
6:16

Complementary and Particular: y''-4y'+4y=2+8x-4x^2- Undetermined Coefficients -Differential Equation

Complementary and Particular: y''-4y'+4y=2+8x-4x^2- Undetermined Coefficients -Differential Equation #DifferentialEquations #ComplementarySolutions #UndeterminedCoefficients
87
Calculus: Complementary and Particular Solutions: y'' - y' - 2y = e^(3x) - Differential Equations
4:57

Calculus: Complementary and Particular Solutions: y'' - y' - 2y = e^(3x) - Differential Equations

Calculus: Complementary and Particular Solutions: y'' - y' - 2y = e^(3x) - Differential Equations #DifferentialEquations #ComplementaryAndParticularSolutions #UndeterminedCoefficients
88
Undetermined Coefficients: Differential Equations -y''+9y=2cos2x- Complementary/Particular Solutions
6:50

Undetermined Coefficients: Differential Equations -y''+9y=2cos2x- Complementary/Particular Solutions

Undetermined Coefficients: Differential Equations -y''+9y=2cos2x- Complementary/Particular Solutions #DifferentialEquations #UndeterminedCoefficients #CalculusHelp
89
Calculus Help: Find the arc length y=4/3 x^(3/2) on the interval [0,1]
2:27

Calculus Help: Find the arc length y=4/3 x^(3/2) on the interval [0,1]

Here is the technique to solve the question and find the arc length #ArcLength #Calculus #Formula
90
Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x
4:52

Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x

Calculus Help: Find the area between the curve y=x^2 and y=-x^2 + 18x #Calculus #Integral #Integrations #Area
91
Calculus Help: ∫ 1/√(1+9x^2 ) dx - Integration by trigonometric substitution - Step-by-step
2:26

Calculus Help: ∫ 1/√(1+9x^2 ) dx - Integration by trigonometric substitution - Step-by-step

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Calculus #Formula
92
Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table
2:02

Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table

Calculus Help: Integral of x^2 sinx dx - Integration by parts by using the table #Integral #Integrations #Calculus #Parts #IntegrationByParts
93
Calculus Help: The cost function, in dollars, of a company that manufactures food
1:54

Calculus Help: The cost function, in dollars, of a company that manufactures food

The cost function, in dollars, of a company that manufactures food processors is given by C(x)=250+6/x+x^2/5 where x is the number of food processors manufactured a) Find the marginal cost function b) F'(11) #Derivative #Calculus #ApplicationOfDerivative
94
Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6
4:09

Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6

Calculus Help: Use cylindrical shells to find the volume of the solid generated when: y=x^2 1 to 6 #Integral #Integrations #Calculus #Techniques
95
Calculus Help: Find the limits - lim (x→0)⁡(1/tanx-1/sinx) - Techniques - SOLVED!!
2:24

Calculus Help: Find the limits - lim (x→0)⁡(1/tanx-1/sinx) - Techniques - SOLVED!!

Calculus Help: Find the limits - lim (x→0)⁡(1/tanx-1/sinx) - Techniques - SOLVED!! #Limits #Functions #Calculus #Techniques
96
Vietnam High School Math Grade 12: Elon Musk had developed the rockets that could allow to return
6:46

Vietnam High School Math Grade 12: Elon Musk had developed the rockets that could allow to return

Elon Musk had developed the rockets that could allow to return back the rocket launch station There are 2 scenarios below.Find the rate of change of the angle of audience . Let a is the rate of change (rad/km) after launching and b is the rate of change (rad/km) before going back the station Find a^2+b (Round the final result by one decimal place) #HighSchoolMath #Grade12 #ApplicationOfDerivative #Derivative
97
If the function f(x) has continuous derivative, 2f(x)+3f(1-x)=√(1-x^2 ) then ∫_0^1 f'(x) dx
2:18

If the function f(x) has continuous derivative, 2f(x)+3f(1-x)=√(1-x^2 ) then ∫_0^1 f'(x) dx

If the function f(x) has continuous derivative on [0;1] and satisfies the condition 2f(x)+3f(1-x)=√(1-x^2 ) then calculate ∫_0^1 f'(x) dx A.I=0 B.I=1 C.I=1/2 D.I=3/2 #CalculusHelp #Integral #Integrations #Solutions
98
Find the approximation of c such that ∫ from c to x f(t) dt = x^3 + 3x^2 + 2x - 3
3:02

Find the approximation of c such that ∫ from c to x f(t) dt = x^3 + 3x^2 + 2x - 3

#Integral #Integrations #Antiderivative
99
Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution
3:03

Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution

Calculus Help: ∫ dx/(x^2 √(a^2-x^2 )) - Integration by trigonometric substitution #CalculusHelp #Integrals #Integrations #TrigonometricSubstitution #Substitution
100
Calculus Help The upper right-hand corner of a piece of paper, 30 centimeters by 20 centimeters fold
7:13

Calculus Help The upper right-hand corner of a piece of paper, 30 centimeters by 20 centimeters fold

The upper right-hand corner of a piece of paper, 30 cm by 20 cm, as in the figure, is folded over to the bottom edge. How would you fold it so as to minimize the length of the fold? In other words, how would you choose x to minimize y? #Calculus #Derivative
101
Calculus Help: Find the limits - lim(x→1)⁡ (x-√(2-x^2 ))/(2x-√(2+2x^2 )) - Techniques
2:57

Calculus Help: Find the limits - lim(x→1)⁡ (x-√(2-x^2 ))/(2x-√(2+2x^2 )) - Techniques

Calculus Help: Find the limits - lim(x→1)⁡ (x-√(2-x^2 ))/(2x-√(2+2x^2 )) - Techniques #Calculus #Limits #Functions #Techniques
102
Calculus Help: Integral ∫ tanx/tan2x dx - Integration by basic trigonometry - Techniques
1:43

Calculus Help: Integral ∫ tanx/tan2x dx - Integration by basic trigonometry - Techniques

Here is the technique to solve Integral tanx/tan2x dx - Integration by basic trigonometry - Techniques #Integral #Integrations #Calculus #Techniques
103
Calculus Help: Integral ∫ cos^2 ⁡x dx and ∫ sin^2 ⁡x dx - Integration by Trigonometric identities
2:13

Calculus Help: Integral ∫ cos^2 ⁡x dx and ∫ sin^2 ⁡x dx - Integration by Trigonometric identities

Here is the technique to solve this question and how to find the question #Calculus #Integrals #Integrations #Solutions #TrigonometricSubstitution
104
Calculus Help: Application of Parabola and Integration (Arc Length) - Ballistic Missile - Red Alert
22:36

Calculus Help: Application of Parabola and Integration (Arc Length) - Ballistic Missile - Red Alert

Here is the technique to solve this question related to the parabolic projectile and find the distance of the ballistic missile after reaching the target. #Calculus #BallisticMissile #Missile #ArcLength #Techniques #Solutions #Formula
105
Calculus Help: Integral of dx/√(1+x^2 ) - Integration by trigonometric substitution
5:49

Calculus Help: Integral of dx/√(1+x^2 ) - Integration by trigonometric substitution

Here is the technique to trigonometric substitution and how to solve it #Integral #integration #Technique #Calculus #Formula #Solution #Technique #Answer
106
Calculus Help: Integral ∫ x √(x^2+4) dx - Integration by substitution - 置換積分
1:46

Calculus Help: Integral ∫ x √(x^2+4) dx - Integration by substitution - 置換積分

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Solutions #Calculus
107
Calculus Help: ∫ x/√(x^2+4) dx - Integration by substitution
0:58

Calculus Help: ∫ x/√(x^2+4) dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
108
Calculus Help: Differential Equations - (6y^3-xy-y)dx+2x dy=0 Bernoulli' s Equation
4:16

Calculus Help: Differential Equations - (6y^3-xy-y)dx+2x dy=0 Bernoulli' s Equation

Here is the technique to solve this differential equations and how to find them in step-by-step #DifferentialEquations #IntegratingFactor #LinearODE #OrdinaryDifferentialEquations
109
Calculus Help: Reduction Variables - y'=(x+y)/(1-3x-3y) - Techniques - SOLVED!!!
5:41

Calculus Help: Reduction Variables - y'=(x+y)/(1-3x-3y) - Techniques - SOLVED!!!

Here is the technique to solve differential equations by Reduction Variables - y'=(x+y)/(1-3x-3y) - Techniques - SOLVED!!! #DifferentialEquations #Calculus #Formula #Techniques
110
Calculus Help: Separable Differential Equations - y'=y/(x-√x) ,y(4)=e - Techniques
3:27

Calculus Help: Separable Differential Equations - y'=y/(x-√x) ,y(4)=e - Techniques

Separable Differential Equations - y'=y/(x-√x) ,y(4)=e - Techniques Here is the technique to solve this differential equation and how to find them in step-by-step #Integral #Integrations #DifferentialEquations #Calculus
111
Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution
3:42

Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution

Calculus Help: Integral ∫ √(1-x^2 )/x^4 dx - Integration by trigonometric substitution #Integral #Integrations #Substitution #TrigonometricSubstitution
112
Calculus Help: Find the limits - lim (x→0^+ )⁡ (1/x-1/(e^x-1)) - Techniques - Solutions
3:30

Calculus Help: Find the limits - lim (x→0^+ )⁡ (1/x-1/(e^x-1)) - Techniques - Solutions

Here is the technique to solve this limit and how to find them in step-by-step #Limits #Functions #Calculus
113
Calculus Help: ∫ ∛x/(∛x+1) dx, ∫ 1/(1+√3x) dx - Integration by substitution - Techniques
4:49

Calculus Help: ∫ ∛x/(∛x+1) dx, ∫ 1/(1+√3x) dx - Integration by substitution - Techniques

Here is the technique to solve these 2 integrals and how to find them in step-by-step #Calculus #Integrals #Integrations #substitution #integrationbysubstitution
114
Calculus Help: Find the limits - lim (x→4)⁡ (x^2-16)/sin⁡(x-4) - Techniques
1:29

Calculus Help: Find the limits - lim (x→4)⁡ (x^2-16)/sin⁡(x-4) - Techniques

Here is the technique to solve this limit and how to find them in step-by-step #Integrals #Integration #Limits #Calculus
115
Calculus Help: A Norman window is constructed by adjoining a semicircle to the top of an ordinary
7:01

Calculus Help: A Norman window is constructed by adjoining a semicircle to the top of an ordinary

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Derivative #ApplicationOfDerivative #Calculus
116
Calculus Help: Find the limits - lim (x→0)⁡ (cosx-1)/x^2 - Techniques - SOLVED!!!
2:11

Calculus Help: Find the limits - lim (x→0)⁡ (cosx-1)/x^2 - Techniques - SOLVED!!!

Here is the technique to solve the limit and how to find them in step-by-step #Limits #Calculus #Formula #Techniques
117
Calculus Help: Basic Integral ∫ √(3x-10) dx - Integration - Techniques
1:41

Calculus Help: Basic Integral ∫ √(3x-10) dx - Integration - Techniques

Here is the technique to solve this integration and how to find them #Integrals #Integrations #Calculus #Basic Transcript
118
Calculus Help: Integral of lnx/x^2 dx - Integration by parts - Techniques
1:34

Calculus Help: Integral of lnx/x^2 dx - Integration by parts - Techniques

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
119
Calculus Help: Integral ∫ x sin⁡(3x) dx - Integration by parts - Techniques - Solutions
1:55

Calculus Help: Integral ∫ x sin⁡(3x) dx - Integration by parts - Techniques - Solutions

Here is the technique to solve this integration by parts and how to find them in step-by-step #Integrals #Integrations #Calculus #Formula
120
Calculus Help: Integral of ∫ e^ax cos⁡(bx)dx - Integration by parts and techniques
3:40

Calculus Help: Integral of ∫ e^ax cos⁡(bx)dx - Integration by parts and techniques

Here is the technique to solve this integral and how to find them in step-by-step #Integrals #Integrations #IntegrationByParts #Calculus #Formula
121
Calculus Help: Integral ∫ x^2 cos⁡(2x) dx - Integration by parts - Techniques - SOLVED!!!
3:01

Calculus Help: Integral ∫ x^2 cos⁡(2x) dx - Integration by parts - Techniques - SOLVED!!!

Here is the technique to solve the question and how to find by integration by parts #Integrals #Integration #Calculus #Formula #Techniques #IntegrationByParts
122
Calculus Help: Integral ∫ xe^(1/2 x) dx - Integration by parts - Techniques
1:53

Calculus Help: Integral ∫ xe^(1/2 x) dx - Integration by parts - Techniques

Here is the technique to solve the question and integration by parts #IntegrationByParts #Techniques #Solutions #Calculus #Integrals #Integrations
123
Calculus Help: Find the limits - lim (x→2)⁡ (x^2-2x)/(x^2-x-2) - Techniques - SOLVED!!!
1:27

Calculus Help: Find the limits - lim (x→2)⁡ (x^2-2x)/(x^2-x-2) - Techniques - SOLVED!!!

Here is the technique to solve the limit and how to find them in step-by-step #Limits #Functions #Calculus
124
Calculus Help: Find the limit - Techniques - lim(x→0)⁡ x^2/(cosx-1)
2:25

Calculus Help: Find the limit - Techniques - lim(x→0)⁡ x^2/(cosx-1)

Here is the technique to solve this limit and how to find them in step-by-step #Limits #CalculusHelp #Techniques
125
Integral ∫ From 2 to 4 √(ln⁡(9-x) )/(√(ln⁡(9-x) )+√(ln⁡(3+x))) dx - Integration by substitution
4:19

Integral ∫ From 2 to 4 √(ln⁡(9-x) )/(√(ln⁡(9-x) )+√(ln⁡(3+x))) dx - Integration by substitution

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Calculus #Formula #Substitution #Integrals #Integrations
126
Calculus Help: Find the limits - lim (x→0) (1-cosx)/sin2x - Techniques - SOLVED!!!
2:27

Calculus Help: Find the limits - lim (x→0) (1-cosx)/sin2x - Techniques - SOLVED!!!

Here is the technique to solve this limit and how to find them in step-by-step #Limits #Functions #Calculus
127
Find the derivative of inverse trigonometry: y=ln⁡(arccos⁡(sinx) ) - Techniques
1:50

Find the derivative of inverse trigonometry: y=ln⁡(arccos⁡(sinx) ) - Techniques

Here is the technique to solve this question and how to find them in step-by-step #Trigonometry #InverseFunctions #InverseTrigonometry #Calculus #Derivative
128
Calculus Help: Integral ∫ cot^3⁡ x csc^4 ⁡x dx - Integration with Substitution - trigonometry
1:58

Calculus Help: Integral ∫ cot^3⁡ x csc^4 ⁡x dx - Integration with Substitution - trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Trigonometry #Antiderivative
129
Calculus Help: Integral of ∫ cot^5⁡ x dx - Integration by substitution - Trigonometry
3:42

Calculus Help: Integral of ∫ cot^5⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula #Solutions
130
Calculus Help: Integral ∫ tan^6 ⁡x sec^4⁡ x dx - Integration by substitution - Trigonometry
1:50

Calculus Help: Integral ∫ tan^6 ⁡x sec^4⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve the integration and how to find #Integral #Antiderivative #Integrations #Calculus #Trigonometry
131
Calculus Help: Integral of ∫ tan^6⁡ x dx - Integration by substitution - Trigonometry
3:38

Calculus Help: Integral of ∫ tan^6⁡ x dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula
132
Calculus Help: Basic Derivative - Introduction: Derivative √(x^2+5)
1:14

Calculus Help: Basic Derivative - Introduction: Derivative √(x^2+5)

Here is the technique to solve this question and how to find them in step-by-step #Derivative #Calculus #Introduction
133
Derivative Help: Introduction of Calculus: y = √((9-x^2)/x^2 )
1:38

Derivative Help: Introduction of Calculus: y = √((9-x^2)/x^2 )

Here is the technique to solve this derivative and how to find them in step-by-step #Derivative #Calculus #Introduction #Solutions
1 comment
134
Polar Coordinates: Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes
8:36

Polar Coordinates: Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes

Evaluate the volume of the cylinder x^2+z^2=9, bounded by the planes x=0, y=0, z=0 and x+2y=2 on first octant Here is the technique to solve the question related to polar coordinates and how to find them in step-by-step #Calculus #Techniques #PolarCoordinates #TripleIntegrals
135
Calculus Help: Integral ∫ sin⁡(2-6x) dx - Basic Integration
0:55

Calculus Help: Integral ∫ sin⁡(2-6x) dx - Basic Integration

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Solutions #Answered
136
Introduction to Calculus Find the derivative by definition - Derivative by definition y=2/x^2
2:31

Introduction to Calculus Find the derivative by definition - Derivative by definition y=2/x^2

Here is the technique to solve and find the derivative by definition #Derivative #Techniques #Solutions #Calculus
137
Introduction of Calculus Basic Derivative: y = (x^2+4x+5)/x - Step-by-step - Power
1:22

Introduction of Calculus Basic Derivative: y = (x^2+4x+5)/x - Step-by-step - Power

Here is the technique to solve the question related to calculus and how to find them in step-by-step #Calculus #Derivative #Solutions
138
Introduction of Calculus First Derivative of Trigonometry and Inverse Trigonometry
9:56

Introduction of Calculus First Derivative of Trigonometry and Inverse Trigonometry

Here is the technique to solve these questions related to Calculus and Derivative #Derivative #Calculus #Solutions
139
Introduction to Calculus: Basic First Derivative - Technique to solve - Step-by-step
9:41

Introduction to Calculus: Basic First Derivative - Technique to solve - Step-by-step

Here is the technique to solve these questions about Derivative and how to find them in step-by-step #Derivative #Calculus #Basic #Techniques
140
Prove inverse trigonometry - sin^(-1)⁡ x =tan^(-1)⁡ ( x/√(1-x^2 ) or arcsinx = arctan(x/√(1-x^2)
4:17

Prove inverse trigonometry - sin^(-1)⁡ x =tan^(-1)⁡ ( x/√(1-x^2 ) or arcsinx = arctan(x/√(1-x^2)

Here is the technique to find the derivative of inverse trigonometry and how to find them in step-by-step #InveseFunction #Function #Techniques
141
Calculus Help: Integral of sin^3⁡ x cosx dx - Integration by substitution
0:56

Calculus Help: Integral of sin^3⁡ x cosx dx - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Calculus #Substitution
142
Calculus Help: ∫ √(16-9x^2 ) dx - Integration by trigonometric substitution
3:58

Calculus Help: ∫ √(16-9x^2 ) dx - Integration by trigonometric substitution

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Calculus #Formula #TrigonometricSubstitution
143
Integration by Substitution: ∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx
5:30

Integration by Substitution: ∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx

∫ (7x+4)^5 dx, ∫ e^x/(2e^x+3)^7 dx, ∫ (x^2+2x)/(x^3+3x^2-4) dx Here is the technique to solve these integrations and how to find them in step-by-step #Integrals #Integrations #Antiderivative #Solutions #Substitution #IntegrationBySubstitution
144
Introduction of Integration: Calculus - ∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx
2:12

Introduction of Integration: Calculus - ∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx

∫ (x^2+1/(2x)^3 )dx ∫ (7x^4+8x^3+9^x )dx ∫ (3 csc^2⁡x-5secx tanx) dx #Calculus #Integrals #Integrations #Introduction
145
lim(x→∞)⁡ ln⁡(√x)/x^2, lim(x→0)⁡ (x 3^x)/(3^x+1), lim(x→∞) √xe^(-x/2), lim(x→1^+ )⁡ lnx tan⁡(πx/2)
6:20

lim(x→∞)⁡ ln⁡(√x)/x^2, lim(x→0)⁡ (x 3^x)/(3^x+1), lim(x→∞) √xe^(-x/2), lim(x→1^+ )⁡ lnx tan⁡(πx/2)

Here is the technique to solve these 4 questions and how to find them in step-by-step #Techniques #Integrals #Limits #Solutions
146
Calculus Help: Derivative by Limit Definition - f'(-1) with f(x)=4/(3x+5 ), f'(2) f(x)=5x^2-2x-3
6:31

Calculus Help: Derivative by Limit Definition - f'(-1) with f(x)=4/(3x+5 ), f'(2) f(x)=5x^2-2x-3

Here is the technique to solve this question of Limit by definition #Limit #Functions #Calculus
147
The Hardest High School Math by Trigonometric Substitution in Vietnam - Integral with long series
10:59

The Hardest High School Math by Trigonometric Substitution in Vietnam - Integral with long series

Here is the technique to solve the integral Integral ( 1 + tan^2 x)(1 + tan^3 x)...(1 + tan^2020 x) + ... + (1+tanx)(1 + tan^2 x)... (1 + tan^2019 x) / (1 + tanx)(1 + tan^2 x)(1 + tan^3 x) ... (1+tan^2020 x) dx #Integral #Integrations #Calculus #TheHardestHighSchoolMath #TrigometricSubstitution
148
Transform the polar equation:r=4cosθ/(cos^2⁡θ+1) into its Cartesian form and identify the curve
3:30

Transform the polar equation:r=4cosθ/(cos^2⁡θ+1) into its Cartesian form and identify the curve

Here is the technique to solve the question related to polar coordinates and how to find them in step-by-step #PolarCoordinates #Calculus #CartesianForm #Solutions
149
Exponential Growth: In a study of an insect population, there were about 118 insects four weeks
4:36

Exponential Growth: In a study of an insect population, there were about 118 insects four weeks

In a study of an insect population, there were about 118 insects four weeks after the study began and about 295 insects after two more weeks. Assuming an exponential model, how many insects in the initial population? #ExponentialGrowth #LogarithmicFunction #Calculus #Insect
150
Calculus Help: Find the limits - lim (x→0)⁡ (1-cosx)/sinx - Techniques - SOLVED!!!
2:06

Calculus Help: Find the limits - lim (x→0)⁡ (1-cosx)/sinx - Techniques - SOLVED!!!

Here is the technique to solve this limit without using L'Hospital #Limits #Calculus #Techniques #Maths
151
Calculus Convergent and Divergent ∑(n=1)^∞ 1/2^n ∑_(n=1)^∞ sinh⁡(n)/cosh⁡(2n) : Ratio, Integral Test
5:14

Calculus Convergent and Divergent ∑(n=1)^∞ 1/2^n ∑_(n=1)^∞ sinh⁡(n)/cosh⁡(2n) : Ratio, Integral Test

Here is the technique to solve two questions related to the series about convergent or divergent #Convergent #Divergent #Techniques #Calculus
152
Calculus Help: Divergent and Convergent Test: Root Test: ∑_(n=1) to ∞ n/(ln⁡ n )^n
1:36

Calculus Help: Divergent and Convergent Test: Root Test: ∑_(n=1) to ∞ n/(ln⁡ n )^n

Here is the technique to find convergent or divergent of the function/the series #Convergent #Divergent #Calculus #RootTest
153
Determine if the equation is exact and if so find the solution: -xy^2-4xy+(-x^2 y-2x^2+3)dy/dx=0
4:14

Determine if the equation is exact and if so find the solution: -xy^2-4xy+(-x^2 y-2x^2+3)dy/dx=0

Here is the technique to solve this differential equation and how to find them in step-by-step #DifferentialEquations #ExactDifferentialEquations
154
Determine whether the given equation is exact (2y-1/x+cos(3x) dy/dx +y/x^2-4x^3-3ysin(3x)=0
2:10

Determine whether the given equation is exact (2y-1/x+cos(3x) dy/dx +y/x^2-4x^3-3ysin(3x)=0

Here is the technique to solve this question related to exact differential equation and how to find them in step-by-step #DifferentialEquations #Exact #ExactDifferentialEquations
155
Calculus Help: Exact Differential Equations: 3y^3 dx+9xy^2 dy=0 - Techniques
3:13

Calculus Help: Exact Differential Equations: 3y^3 dx+9xy^2 dy=0 - Techniques

Here is the technique to solve this differential equation and how to find them in step-by-step #DifferentialEquations #Calculus #ExactDifferentialEquations
156
Calculus: Differential Equation - y' = y-xy^3 e^(-2x) - Integrating Factor - Bernoulli's Equation
4:29

Calculus: Differential Equation - y' = y-xy^3 e^(-2x) - Integrating Factor - Bernoulli's Equation

Here is the technique to solve this differential equation and how to find them in step-by-step #DifferentialEquations #CalculusHelp #IntegratingFactor #Bernoulli
157
Differential Equations: Linear ODE - Integrating Factor - dy/dx- y=11/8 e^(-x/3)
2:51

Differential Equations: Linear ODE - Integrating Factor - dy/dx- y=11/8 e^(-x/3)

Here is the technique to solve the question about differential equations and how to find them in step-by-step #Techniques #IntegratingFactor #LinearODE #Calculus
158
Calculus Help: Find the limits - lim (x→0)⁡ x cotx - Techniques - SOLVED!!!
1:15

Calculus Help: Find the limits - lim (x→0)⁡ x cotx - Techniques - SOLVED!!!

Here is the technique to solve this question with basic L'Hospital #LHospital #Calculus #Derivative #Limits
159
Calculus Help: Find the limits: lim (x→0)⁡ (tanx-sinx)/x^3 - Technique to solve
3:15

Calculus Help: Find the limits: lim (x→0)⁡ (tanx-sinx)/x^3 - Technique to solve

Here is the technique to solve this limit and how to find #LHospital #Limit #Calculus #Derivative
160
Differential Equations: Transform into exact: 6x(x^2+1)y+4xy^2+((x^2+1)^2+2y(x^2+1)) dy/dx=0
13:07

Differential Equations: Transform into exact: 6x(x^2+1)y+4xy^2+((x^2+1)^2+2y(x^2+1)) dy/dx=0

Here is the technique to solve this question and how to find them in step-by-step #DifferentialEquations #Calculus #Exact #ExactDifferentialEquations
161
Calculus Help: Separable Differential Equations -> dy/dx = -y/x , y(1) = 2
1:30

Calculus Help: Separable Differential Equations -> dy/dx = -y/x , y(1) = 2

Here is the technique to solve this differential equation and how to find them in step-by-step #DifferentialEquations #Calculus #CalculusHelp #Techniques
162
Integral: 3 sin⁡(2x) ; 5 sin⁡(3x) cos^3⁡ (3x) ; e^2x/(e^2x+3) ; x√(x+3) ; (x)/∛(x+1) ∫1/(x√(7-x^2 ))
10:13

Integral: 3 sin⁡(2x) ; 5 sin⁡(3x) cos^3⁡ (3x) ; e^2x/(e^2x+3) ; x√(x+3) ; (x)/∛(x+1) ∫1/(x√(7-x^2 ))

Here is the technique to solve these integrations and how to find them in step-by-step #Integrals #Integrations #Calculus
163
Calculus Techniques: Integration ∫ 1 dx/(1+tanx) - Integration by substitution - SOLVED!!
4:26

Calculus Techniques: Integration ∫ 1 dx/(1+tanx) - Integration by substitution - SOLVED!!

Here is the technique to solve this integration and how to find them #Integral #Integration #Calculus #Formula #Techniques
164
Calculus Help: Integrating Factor - Linear ODE: 3(y+1)dx=2xdy
3:55

Calculus Help: Integrating Factor - Linear ODE: 3(y+1)dx=2xdy

Here is the technique to solve this integration factor and how to solve the linear ODE #LinearODE #IntegratingFactor #DifferentialEquations
165
Calculus Help: For the function f(x)=2√(-4x^6 + 6e^x) find f'(x)
2:11

Calculus Help: For the function f(x)=2√(-4x^6 + 6e^x) find f'(x)

Here is the technique to solve this derivative of the function #Function #Derivative #Techniques
166
Geometry Help: Find the equation of the line passing through (5,2)and perpendicular to the line
2:31

Geometry Help: Find the equation of the line passing through (5,2)and perpendicular to the line

Here is the technique to solve this question and how to find them in step-by-step with derivative and perpendicular #Perpendicular #Parallel #Calculus
167
Calculus Help: f(x)=√(x^2-4) , g(x)=1/√(x^2-1) Find fog and gof .Find domains and composition
8:10

Calculus Help: f(x)=√(x^2-4) , g(x)=1/√(x^2-1) Find fog and gof .Find domains and composition

Here is the technique to solve the composition and find the domains with ranges in 2 functions #Domain #Range #Composition #Calculus
168
Calculus Help: Basic Integral - Integral of x^2025 dx - Basic Formula
0:48

Calculus Help: Basic Integral - Integral of x^2025 dx - Basic Formula

Here is the technique to solve the basic Integration and how to find them in step-by-step
169
Calculus Help: Eliminate the arbitrary constants: y= C1 e^(3x) + C2 e^(2x) + C3 e^x - Techniques
2:20

Calculus Help: Eliminate the arbitrary constants: y= C1 e^(3x) + C2 e^(2x) + C3 e^x - Techniques

Here is the basic way to do elimination of the arbitrary constants for differential equations #DifferentialEquations #ArbitraryConstants #Techniques #Calculus
170
Calculus Help: How to find the graph of function: Asymptotes and y-intercept
3:40

Calculus Help: How to find the graph of function: Asymptotes and y-intercept

Here is the full video to answer the question and how to find the graph of the function #Graph #Functions #Asymptotes
171
Integral Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Solutions
4:45

Integral Help: ∫ √(1+x^2 )/x dx - Integration by trigonometric substitution - Solutions

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integrations #Solutions
172
Calculus Help: Integral from 4 to 7 - dx/(x^2-5x+6) - Techniques - Partial Fractions
3:18

Calculus Help: Integral from 4 to 7 - dx/(x^2-5x+6) - Techniques - Partial Fractions

Here is the technique to solve this question and how to find them in step-by-step #PartialFractions #Integrations #Integrals #Calculus
173
Integral Help: ∫ Integration from 5 to 10 x^2 lnx dx - Integration by parts - Techniques in Cal
2:10

Integral Help: ∫ Integration from 5 to 10 x^2 lnx dx - Integration by parts - Techniques in Cal

Here is the full video to show how to solve the integration and how to find them in step-by-step #Integrals #Integrations #Parts #Answered
174
Calculus Help: Integration from 4 to 9 √x/(√x-1) dx - Techniques - Integration by substitution
3:25

Calculus Help: Integration from 4 to 9 √x/(√x-1) dx - Techniques - Integration by substitution

Here is the full video to solve this question and how to find them in step-by-step #Integrals #Integrations #Solutions #Calculus
175
Calculus Help: Find the limits lim (x→64)⁡ (√x-8)/(∛x-4) - lim(x→6)⁡ (2-√(x-2))/(x^2-36)
6:47

Calculus Help: Find the limits lim (x→64)⁡ (√x-8)/(∛x-4) - lim(x→6)⁡ (2-√(x-2))/(x^2-36)

Here is the technique to solve 3 limits and how to solve them in here: lim┬(x→64)⁡〖(√x-8)/(∛x-4)〗 lim┬(x→6)⁡〖(2-√(x-2))/(x^2-36)〗 lim┬(x→9)⁡〖(2x^5-162x^3)/(x^5-6x^4-27x^3 )〗 #Calculus #Techniques #Solutions #Answers
176
Calculus Help: Cauchy-Reimann Equations : 1/z - Step-by-step - Derivative of Complex Numbers
8:05

Calculus Help: Cauchy-Reimann Equations : 1/z - Step-by-step - Derivative of Complex Numbers

Here is the technique to solve this equation and how to find them #Solving #ComplexNumbers #Solutions #Reimann #Cauchy
177
Calculus Help: Find the Integral of (2x^2+4x-3)/x^2 dx - Techniques - Solutions
2:52

Calculus Help: Find the Integral of (2x^2+4x-3)/x^2 dx - Techniques - Solutions

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered
178
Calculus Help: Find the limits: lim (x→3)⁡ (x^3-27)/(x^2-9) - Technique to solve
2:09

Calculus Help: Find the limits: lim (x→3)⁡ (x^3-27)/(x^2-9) - Technique to solve

Here is the technique to solve this question and how to find them in step-by-step #Calculus #Limit #Solutions
179
Calculus Help: Integral of (x+1)dx/(x^3+x^2-6x) - Integration by partial fractions
4:52

Calculus Help: Integral of (x+1)dx/(x^3+x^2-6x) - Integration by partial fractions

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered #PartialFractions
180
Calculus Help: Integrals: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9
3:14

Calculus Help: Integrals: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9

Full question: A solid lies between planes perpendicular to the x-axis at x = 0 and x=9. The cross sections perpendicular to the x-axis between these planes are squares whose bases run from the parabola y = - 4√x to the parabola y = 4√x. Find the volume of the solid #CalculusHelp #CrossSection #Integral
181
Calculus Help: Integral ∫ x^3/(4x^2+9)^(3/2) dx - Integration by substitution - Techniques
3:53

Calculus Help: Integral ∫ x^3/(4x^2+9)^(3/2) dx - Integration by substitution - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Solutions #Answered #Substitution
182
Integral: ∫ dx/(e^x - 1) and how to solve - Integration - Step-by-step
3:19

Integral: ∫ dx/(e^x - 1) and how to solve - Integration - Step-by-step

Here is the technique to solve this integration and how to find them in step-by-step #Integral #Integration #Step-by-step #Calculus
183
Calculus Help: Triple Integrals - ∫ From 0 to 1 ∫ From 0 to 1 ∫ From 0 to 1 e^(x+y+z) dx dy dz
2:22

Calculus Help: Triple Integrals - ∫ From 0 to 1 ∫ From 0 to 1 ∫ From 0 to 1 e^(x+y+z) dx dy dz

Here is the technique to solve this question and how to find them in step-by-step #Techniques #Integrals #Integrations #TripleIntegrals
184
Calculus Help: ∫ x^3 sinx dx - Integration by parts - Techniques - Solutions
4:09

Calculus Help: ∫ x^3 sinx dx - Integration by parts - Techniques - Solutions

Here is the technique to solve this integration and how to find them in here by integration by parts #Integral #Integration #Calculus #Formula #Solutions
185
Calculus Help: Apply L'Hospital and How to solve it lim {x→1/2}⁡(tan⁡(3πx))/(sec⁡(πx))
3:25

Calculus Help: Apply L'Hospital and How to solve it lim {x→1/2}⁡(tan⁡(3πx))/(sec⁡(πx))

Here is the technique to find this limit and how to solve it #Limit #Calculus #Formula #Techniques
186
A 6-ft-tall person walks away from a 10-ft lamppost at a constant rate of 3ft/sec. What is rate
4:16

A 6-ft-tall person walks away from a 10-ft lamppost at a constant rate of 3ft/sec. What is rate

Full question: A 6-ft-tall person walks away from a 10-ft lamppost at a constant rate of 3ft/sec. What is the rate that the tip of the shadow moves away from the pole when the person is 10ft away from the pole? #Techniques #Calculus #Answered #Solutions
187
Calculus Help: Homogeneous - Differential Equations - ( x-y lny+y lnx) dx+x( lny-lnx )dy=0
7:24

Calculus Help: Homogeneous - Differential Equations - ( x-y lny+y lnx) dx+x( lny-lnx )dy=0

Here is the technique to find all solutions about differential equations and how to find it in step-by-step #DifferentialEquations #Techniques #Solutions #Answered #Homogeneous #Techniques
188
Calculus Help: Integral of ∫ arctan⁡(3x)dx - Integration by parts and how to solve
3:20

Calculus Help: Integral of ∫ arctan⁡(3x)dx - Integration by parts and how to solve

Here is the technique to solve this question and how to find them in step-by-step #Integral #Integrations #Solutions #Answered
189
Calculus Help: sin^2 x dx / sqrt(1-cosx) - sin^2 x dx/ √(1 - cosx) - Integration by substitution
4:30

Calculus Help: sin^2 x dx / sqrt(1-cosx) - sin^2 x dx/ √(1 - cosx) - Integration by substitution

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Integrals #Integration
190
Calculus Help: Integral ∫ (2x^2-x+4)/(x^3+4x) dx - Integration by division - Techniques
5:39

Calculus Help: Integral ∫ (2x^2-x+4)/(x^3+4x) dx - Integration by division - Techniques

Here is the technique to solve this question and how to find them in step-by-step #Calculus #Solutions #Techniques #Division #Integrations
191
Calculus Help: Integral ∫ x/√(36-x^2 ) dx - Integration by trigonometric substitution - 三角関数での置換
2:45

Calculus Help: Integral ∫ x/√(36-x^2 ) dx - Integration by trigonometric substitution - 三角関数での置換

Here is the technique to solve this question and how to find them in step-by-step #三角関数での置換 #Techniques #Solutions #Answer #TrigonometricSubstitution
192
Calculus Help: Integral of cos2x sin3x dx - Integration by Trigonometric identities
2:34

Calculus Help: Integral of cos2x sin3x dx - Integration by Trigonometric identities

Here is the technique to solve and find the value of the function and how to find the function #Calculus #Integral #Integrations #Functions
193
Calculus Help: ∫ sin^4 ⁡x cos^6⁡ x dx - Integration with trigonometry - Equation - Integrals
8:04

Calculus Help: ∫ sin^4 ⁡x cos^6⁡ x dx - Integration with trigonometry - Equation - Integrals

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Solutions #Answered
194
Calculus Help: Find the first three non-zero terms of Maclaurin expansion
2:59

Calculus Help: Find the first three non-zero terms of Maclaurin expansion

Here is the technique to find first three non-zero terms of Maclaurin expansion #MaclaurinExpansion #MaclaurinSeries #Series #Calculus
195
Calculus Help: Differential Equations - dy/dx=(3x+2y)/(3x+2y+2) ,y(-1)=-1 - Reduction Variable
5:56

Calculus Help: Differential Equations - dy/dx=(3x+2y)/(3x+2y+2) ,y(-1)=-1 - Reduction Variable

Here is the technique to solve this question and how to find them in step-by-step: Calculus Help: Differential Equations - dy/dx=(3x+2y)/(3x+2y+2) ,y(-1)=-1 - Reduction Variable #DifferentialEquations #IntegratingFactor #Techniques #Solutions
196
Calculus Help: Differential Equations - dy/dx-tany/(1+x)=(1+x) e^x secy - Techniques
5:38

Calculus Help: Differential Equations - dy/dx-tany/(1+x)=(1+x) e^x secy - Techniques

Here is the technique to solve this differential equations and how to find them in step-by-step #DifferentialEquations #Calculus #Solutions
197
Calculus Help: Integral of cos^3⁡x/(1-sinx) dx - Integration by substitution - Trigonometry
1:44

Calculus Help: Integral of cos^3⁡x/(1-sinx) dx - Integration by substitution - Trigonometry

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Calculus #Solutions #Substitution
198
Calculus Help: Separable Differential Equation: dy/dx=e^(x-y) - Exponent and Power Equation
1:55

Calculus Help: Separable Differential Equation: dy/dx=e^(x-y) - Exponent and Power Equation

Here is the technique to solve the question and how to find this separable differential equation #DiffernetialEquations #Calculus #SeparableDifferentialEquations #Exponent
199
Calculus Help: Integral ∫ sinx √(1+cosx)dx - Integration by substitution - Techniques
2:15

Calculus Help: Integral ∫ sinx √(1+cosx)dx - Integration by substitution - Techniques

Here is the technique to solve this integration and how to find them in step-by-step #Techniques #Calculus #Integrations #Integrals #Solutions
200
Calculus Help: Differential Equation - Transform into Homogeneous - dy/dx=(x+y+4)/(x-y-6)
8:12

Calculus Help: Differential Equation - Transform into Homogeneous - dy/dx=(x+y+4)/(x-y-6)

Here is the technique to solve this question and how to find them in step-by-step Differential Equation - Transform into Homogeneous - dy/dx=(x+y+4)/(x-y-6)

Calculus Help: An object of mass m is dropped into the sea at the surface. It is subject to a

Save
6 months ago
56
Health & Science CalculusHelp Integrals differentialequations PartialFractions

An object of mass m is dropped into the sea at the surface. It is subject to a constant gravitational acceleration g and water resistance. (a) (4 points) If the water resistance is proportional to the object's velocity v(t) with coefficient b ≫ 0, so that Newton's second law gives b dv/dt =g- b/m v show that the object's velocity as a function of time t is given by v(t) = mg/b (1-e^(-bt/m)). We take downward to be the positive direction and the object is at rest when it is dropped at t=0. (b) (4 points) If instead the water resistance is quadratic in the velocity, so that Newton's second law gives dv/dt =g- b/m v^2 dt m dv dt find the object's velocity as a function of time t, again assuming that the object is dropped from rest. [Hint: Write Newtons' law as = g(1 − k^2v^2) where k = √b/mg. Then the algebra is a little less messy. After obtaining the final answer in terms of k, remember to replace k by √b/mg.] (c) (2 points) If the object could fall forever under these conditions without hitting the bottom, show that as t→ ∞ the velocity in part (a) approaches terminal velocity v → mg/b. What terminal velocity does the velocity in part (b) approach?

#CalculusHelp
#Integrals
#differentialequations
#PartialFractions

Loading comments...