Slant Asymptote Lines: Example 2: Horizontal Hyperbola

In this video I go over another example on Slant Asymptotes and this time look at the slant asymptote lines of a horizontal hyperbola, which is a hyperbola that extends outwards horizontally. The hyperbola x^2/a^2 – y^2/b^2 = 1 where a and b are constants has slant asymptote lines y = +/- (b/a)x. This is proven by applying the definition of slant asymptotes which I covered in my earlier video, and that is the limit as x approaches infinity of the difference between the function and a line approaches zero. In other words the function, in this case the hyperbola, approaches the asymptote lines. In proving this, I first rearrange the hyperbola to write it as y = f(x). But since the function involves square rooting a square, we get a two part function that can be either positive or negative, and thus to save time I combined all of the +/- terms (as well as the limit as x approaches +/- infinity) in just one limit formula. This was a shortcut on my part, but nonetheless the result is the same for this particular example as compared with doing it individually. I will be referencing this example on slant asymptotes for a horizontal hyperbola in my later videos, so make sure you watch this video and understand the derivation!

- PDF notes: https://1drv.ms/b/s!As32ynv0LoaIh5E1eR_74BRIMsvEmA
- Hive notes: https://peakd.com/mathematics/@mes/slant-asymptote-lines-example-2-horizontal-hyperbola
- Limits playlist: https://www.youtube.com/playlist?list=PLFE39AF0D7E0651AC

Related Videos:

Slant Asymptote Lines: Example 1: Rational Function: https://youtu.be/FT5yNtPeBvg
Slant Asymptote Lines + Special Case: Rational Functions and Long Division: https://youtu.be/QX2nfi5JtQs
Hyperbola - Definition and derivation of the equation: x^2/a^2 - y^2/b^2 = 1: http://youtu.be/Y6iYC4VEAi0
Limits at Infinity: Horizontal Asymptotes: http://youtu.be/6pdgb09wRvI .

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