Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 14


$$ \lim _{x \rightarrow \infty} e^{x-x^2}=0. $$

Work Step by Step

Since $ x^2-x $ is always positive for all $ x>0$, then we have $$ \lim _{x \rightarrow \infty} e^{x-x^2}=\lim _{x \rightarrow \infty} e^{-(x^2-x)}=0. $$
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