Calculus: Early Transcendentals (2nd Edition)

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

Chapter 2 - Limits - Review Exercises: 32

Answer

$0$

Work Step by Step

$\lim _{x\rightarrow \infty }\dfrac {x^{4}-1}{x^{5}+2}=\lim _{x\rightarrow \infty }\dfrac {x^{4}\left( 1-\dfrac {7}{x^{4}}\right) }{x^{4}\left( x+\dfrac {2}{x^{4}}\right) }=\lim _{x\rightarrow \infty }\dfrac {\left( 1-\dfrac {7}{x^{4}}\right) }{x+\dfrac {2}{x^{4}}}=\lim _{x\rightarrow \infty }\dfrac {1-0}{x+0}=\lim _{x\rightarrow \infty }\dfrac {1}{x}=0$
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