University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 2 - Practice Exercises - Page 111: 51



Work Step by Step

$$A=\lim_{x\to\infty}e^{1/x}\cos\frac{1}{x}$$ $$A=e^{\lim_{x\to\infty}1/x}\cos\Big(\lim_{x\to\infty}\frac{1}{x}\Big)$$ As $x\to\infty$, $1/x$ approaches $0$. Therefore, $$A=e^0\cos0=1\times1=1$$
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