Answer
$2$
Work Step by Step
$\lim_{\theta\to\pi/4}\frac{tan\theta-1}{\theta-\pi/4}=\lim_{\theta\to\pi/4}\frac{tan\theta-tan(\pi/4)}{\theta-\pi/4}=(tan\theta)'|_{\theta=\pi/4}=(sec^2\theta)|_{\theta=\pi/4}=sec^2(\pi/4)=2$
Thomas' Calculus 13th Edition
by Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0-32187-896-5
ISBN 13:
978-0-32187-896-0
Chapter 3: Derivatives - Section 3.5 - Derivatives of Trigonometric Functions - Exercises 3.5 - Page 142: 50
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