Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - True-False Quiz: 20


This is not true.

Work Step by Step

Not true. The counterexample is the function $$f(x)=1+e^{-\frac{1}{x^2}}.$$ This funtion is everywhere greater than $1$ but when $x\to 0$ we have $$\lim_{x\to0}(1+e^{-\frac{1}{x^2}})=\left[1+e^{-\frac{1}{0^+}}\right]=\left[1+e^{-\infty}\right]=1$$ which is not greater than one.
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