lim when x approaching to inf

Question

((1/x+ 1)^x^2) e^-x

evaluate the limit

Answer 1

The left hand part of this expression is exp(x²) in the limit.

Therefore the whole expression approaches exp(x²-x) which is unbounded as x goes to ∞.

Ooops, I made a mistake!!!!!

First you need to review one definition of the number e, which is

lim as x->∞ [1+(1/x)]^x.

Then you can see that the left side of the expression goes to e^X.

Then in the limit you have e^x * e^-x = 1 so that the limit is 1.

Sorry, I made that error.