How does $1/e^{(1/\infty)}$ equal $1$?

Question

My professor had us solve an improper integral, the problem or work I did correctly, however, when I got to the final part of the answer, I got $1/e^{1/\infty} - 1/e$.

My professor got this as well, but when she put the actual value, she put $1 - 1/e$.

I thought that $e^{(-1/\infty)}$ equals zero, because anything over infinity equals zero. Am I wrong? Why does it equal 1?

Answer 1

HINT

Note that $(1)$ $\lim_{x\to \infty }1/x=0$, $(2)$ $e^0=1$, and $(3)$ the exponential function is continuous.

Answer 2

The bit that reads (-1/inf) is equivalent to zero. So now doing the exponential you have exp(0), which of course is 1.

Answer 3

First of all, $\frac{1}{x^{1/\infty}}$ doesn't equal anything because $\infty$ is not a number.

However, $\lim_{x\to\infty} \frac{1}{e^{1/x}}=\frac{1}{e^0}=1$