Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.5 Limits at Infinity - 2.5 Exercises - Page 96: 26


$\lim _{x\rightarrow \infty }\dfrac {3x^{2}-7}{x^{2}+5x}=3;\lim _{x\rightarrow -\infty }\dfrac {3x^{2}-7}{x^{2}+5x}=3;y=3$

Work Step by Step

$\lim _{x\rightarrow \infty }\dfrac {3x^{2}-7}{x^{2}+5x}=\dfrac {3-\dfrac {7}{x^{2}}}{1+\dfrac {5}{x}}=\dfrac {3-0}{1+0}=3$ $\lim _{x\rightarrow -\infty }\dfrac {3x^{2}-7}{x^{2}+5x}=\dfrac {3-\dfrac {7}{x^{2}}}{1+\dfrac {5}{x}}=\dfrac {3-0}{1+0}=3$ So the horizontal asymptote will be $y=3$
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