Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.5 L'Hopital's Rule; Indeterminate Forms - Exercises Set 6.5: 4

Answer

True.

Work Step by Step

Continuing to take the derivative of a polynomial will eventually lead to the term $0$. Therefore, when taking the derivative of the numerator and denominator, the numerator will become zero after a certain amount of derivatives and the denominator will remain as $e^{x}$. Therefore, the limit as $x$ approaches infinity will always be 0.
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