Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 67: 29

Answer

The function $\tan 2t $ is discontinuous at $$ t=\frac{(2n+1)\pi}{4}$$ and the discontinuity is infinite.

Work Step by Step

Since $\tan 2t=\frac{\sin 2t }{\cos 2t}$, then the function is discontinuous when $$\cos 2t =0.$$ That is, $2t=\frac{(2n+1)\pi}{2}$, n is integer. This means that the function $\tan 2t $ is discontinuous at $$ t=\frac{(2n+1)\pi}{4}$$ and the discontinuity is infinite.
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