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: 9

Answer

$1$

Work Step by Step

Since the limit as theta approaches zero is $\frac{0}{0}$, L'Hopital's Rule can be used. The derivative of the numerator and denominator is performed, leaving $$\lim\limits_{\theta \to 0}sec^{2} \theta=sec^{2}(0)=1^{2}=\boxed{1}.$$
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