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: 29


$$\lim _{x\rightarrow \infty }\dfrac {3x^{3}-7}{x^{4}+5x^{2}}=0;\lim _{x\rightarrow -\infty }\dfrac {3x^{3}-7}{x^{4}+5x^{2}}=0;y=0$$

Work Step by Step

$$\lim _{x\rightarrow \infty }\dfrac {3x^{3}-7}{x^{4}+5x^{2}}=\dfrac {\dfrac {3}{x}-\dfrac {7}{x^{4}}}{1+\dfrac {5}{x^{2}}}=\dfrac {0-0}{1+0}=\dfrac {0}{1}=0$$ $$\lim _{x\rightarrow -\infty }\dfrac {3x^{3}-7}{x^{4}+5x^{2}}=\dfrac {\dfrac {3}{x}-\dfrac {7}{x^{4}}}{1+\dfrac {5}{x^{2}}}=\dfrac {0-0}{1+0}=\dfrac {0}{1}=0$$ So the horizontal asymptote will be $y=0$
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