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April 18, 2014

April 18, 2014

Posted by **Sachenka** on Thursday, February 3, 2011 at 7:57pm.

f(x)=(4x^2 -7x +2)/(x^2 -16x +63)

Find the equations of the horizontal asymptotes and the vertical asymptotes of f(x). If there are no asymptotes of a given type, enter NONE. If there is more than one asymptote of a given type, give a comma seperated list (i.e.: 1, 2,...).

- Calculus - asymptotes -
**MathMate**, Friday, February 4, 2011 at 8:04amTo find the vertical asymptotes, factorize the denominator (if possible) and determine the zeroes of the denominator. Here we find two at x=7 and x=9:

f(x)=(4x^2 -7x +2)/(x^2 -16x +63)

=(4x^2 -7x +2)/((x-7)(x-9))

To find horizontal asymptotes, find the limit of the function as x->∞ or x->-∞.

Lim f(x) x->∞

=Lim (4x²-7x+2)/(x²-16x+63)

=LIm (4x²/x²)

=4

Here we found a horizontal aysmptote at y=4

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