Slant Asymptote Lines: Example 2: Horizontal Hyperbola

in Threespeak17 days ago

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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 x2/a2 – y2/b2 = 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!

Download the notes in my video:!As32ynv0LoaIh5E1eR_74BRIMsvEmA

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Related Videos:

Slant Asymptote Lines: Example 1: Rational Function:
Slant Asymptote Lines + Special Case: Rational Functions and Long Division:
Hyperbola - Definition and derivation of the equation: x2/a2 - y2/b2 = 1:
Limits at Infinity: Horizontal Asymptotes: .


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