Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 8 - Sequences and Infinite Series - 8.2 Sequences - 8.2 Exercises: 15

Answer

$\lim\limits_{n \to \infty} tan^{-1} n = \frac{\pi}{2}$

Work Step by Step

To find the limit, we can keep increasing $n$ and see if the function approaches a certain value. $tan^{-1} (0) = 0$ $tan^{-1} (10) =1.471$ $tan^{-1} (100) = 1.561$ $tan^{-1} (1000) = 1.570$ $tan^{-1} (10000) = 1.571$ $tan^{-1} (100000) = 1.571$ Since $tan^{-1} n$ seems to approach $\frac{\pi}{2}$ as $n$ increases, the limit is $\frac{\pi}{2}$.
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