Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 1 - Limits and Continuity - 1.3 Limits At Infinity; End Behavior Of A Function - Exercises Set 1.3 - Page 80: 41

Answer

See explanation

Work Step by Step

Given $p(x)=(1-x)^n$ $\lim\limits_{x \to -\infty} (1-x)^n=+\infty$ $\lim\limits_{x \to +\infty} (1-x)^n$ depends on $n$: if $n$ is odd, the limit is $-\infty$, while if $n$ is even the limit is $+\infty$. This can be written: $\lim\limits_{x \to +\infty} (1-x)^n=(-1)^n\infty$
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