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 83: 31



Work Step by Step

We are given $$g(t)=5^{-1 / t^{2}} $$ We find the limit of the exponent: \begin{align*} \lim _{t \rightarrow \pm \infty}-\frac{1}{t^{2}}&=-\frac{1}{\infty}\\ &=0 \end{align*} Then \begin{align*} \lim _{t \rightarrow \pm \infty} 5^{-1 / t^{2}}&=5^{\lim _{t \rightarrow \pm \infty} -\frac{1}{t^{2}}}\\ &=5^{0}=1 \end{align*}
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