as the limit of t approaches $\displaystyle (pie/2)^{+}$ of
$\displaystyle e^{tan(t)}$
it looks like zero but the back of the book has positive infinity as the answer
The tangent goes to $\displaystyle \infty$ as t approaches $\displaystyle \frac{\pi}{2}$ and the exponential goes to $\displaystyle \infty$ as t approaches $\displaystyle \frac{\pi}{2}$
Graph of tan(x)
Graph of $\displaystyle e^x$
Are you sure this is a right-handed limit?
If this were a right handed limit it would in fact be 0, if it were a left handed limit it would be $\displaystyle \infty$