Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - Chapter 6 Review Exercises - Page 484: 15

$$0$$

$$\eqalign{ & \mathop {\lim }\limits_{t \to \pi /{2^ + }} {e^{\tan t}} \cr & {\text{Evaluate the limit }} \cr & \mathop {\lim }\limits_{t \to \pi /{2^ + }} {e^{\tan t}} = {e^{\mathop {\lim }\limits_{t \to \pi /{2^ + }} \tan t}} \cr & \mathop {\lim }\limits_{t \to \pi /{2^ + }} \tan t = \tan \left( {{{\frac{\pi }{2}}^ + }} \right) = - \infty \cr & {\text{Therefore,}} \cr & {e^{\mathop {\lim }\limits_{t \to \pi /{2^ + }} \tan t}} = {e^{ - \infty }} = 0 \cr & {\text{The following graph confirms the result}} \cr} $$