#### To determine

**To find**:limx→π2+etanx.

#### Answer

0

#### Explanation

Since t=tanx +∞ as xπ2+, limx→π2+etanx=e-∞

We know that tanπ2 was undefined. However, if you look at the graph below. You will see as tangent approaches π2 from the right side, the tangent function in actuality approaches −∞.

We have used the fact that e−∞=1e∞=1∞=0

**Conclusion:** 0