Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 3 - Applications of Differentiation - 3.4 Limits at Infinity; Horizontal Asymptotes - 3.4 Exercises - Page 241: 6

Answer

$$ \lim_{x\to \infty} f(x) \approx 0.135$$

Work Step by Step

(a) Given $$f(x) =\left(1-\frac{2}{x}\right)^x $$ From the figure , it is clear that as $x\to\infty$ $f(x)\to 0.135$ (b) by using values of $x$ , we get $ f(10)=0.107374$, $f(100) =0.135064$, $f(1000) =0.1353327$, and $f(10000) =0.1353352$ , then $$ \lim_{x\to \infty} f(x) \approx 0.135$$
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