So I'm supposed to prove that

And I'm doing so by using the squeezing theorem (with guided help from the book)

I know for certain that

(btw the left is 1 over e to the power of all that stuff, Latex is making it look weird)

This is correct. My book confirmed so. And I can see how the left side of the equation approaches 1/e. Somehow the right side does and I can't see how....anybody?