Answer
$$\lim_{x\to\infty}e^{1/x}\cos\frac{1}{x}=1$$
Work Step by Step
$$A=\lim_{x\to\infty}e^{1/x}\cos\frac{1}{x}$$
$$A=e^{\lim_{x\to\infty}1/x}\cos\Big(\lim_{x\to\infty}\frac{1}{x}\Big)$$
As $x\to\infty$, $1/x$ approaches $0$. Therefore,
$$A=e^0\cos0=1\times1=1$$
