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: 18

Answer

$$\lim_{\theta\to\pi}\frac{1+\cos\theta}{1-\cos\theta}=0$$

Work Step by Step

$$A=\lim_{\theta\to\pi}\frac{1+\cos\theta}{1-\cos\theta}$$ No, you do not need L'Hospital's Rule here. Not because there is an elementary method here, but we can replace $\pi$ into $\theta$ right away. In other words, this is no indeterminate form of any kind. $$A=\frac{1+\cos(\pi)}{1-\cos(\pi)}$$ $$A=\frac{1+(-1)}{1-(-1)}$$ $$A=\frac{0}{2}$$ $$A=0$$
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