Answer
$$\lim\limits_{x\to\infty}\arctan(e^x)=\frac{\pi}{2}$$
Work Step by Step
$$A=\lim\limits_{x\to\infty}\arctan(e^x)$$
Let $t=e^x$. As $x\to\infty$, $e^x$ approaches $\infty$. Therefore, $t\to\infty$.$$A=\lim\limits_{t\to\infty}\arctan(t)$$$$A=\frac{\pi}{2}$$
*NOTES TO REMEMBER: $\lim\limits_{x\to\infty}\arctan(x)=\frac{\pi}{2}$
