Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.7 Limits at Infinity - Exercises - Page 82: 3

Answer

$f(x)=\dfrac{3x^2}{x^2+7}$

Work Step by Step

An example of a function with one horizontal asymptote is $f(x)=\dfrac{P(x)}{Q(x)}$, where $P(x)$ and $Q(x)$ are polynomials having the same degree, $Q(x)≠0$ and the coefficient of the term of highest degree in the numerator is 3 times the the coefficient of the term of highest degree in the denominator. For example: $f(x)=\dfrac{3x^2}{x^2+7}$ The horizontal asymptote is: $y=\dfrac{3}{1}=3$
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