Calculus: Early Transcendentals 8th Edition

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

Chapter 4 - Section 4.4 - Indeterminate Forms and l''Hospital''s Rule - 4.4 Exercises - Page 312: 73


$\lim\limits_{x \to \infty}\frac{e^x}{x^n} = \infty$

Work Step by Step

We can use L'Hospital's Rule: $\lim\limits_{x \to \infty}\frac{e^x}{x^n}$ $=\lim\limits_{x \to \infty}\frac{e^x}{nx^{n-1}}$ $=\lim\limits_{x \to \infty}\frac{e^x}{(n)(n-1)x^{n-2}}$ $=\lim\limits_{x \to \infty}\frac{e^x}{(n)(n-1)(n-2)x^{n-3}}$ $= ...$ $=\lim\limits_{x \to \infty}\frac{e^x}{(n)(n-1)(n-2)...(3)(2)(1)}$ $= \infty$
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