This can be done any number of ways. Here is one, first note that . Here I will use . If you would like to prove this to yourself try finding the absolute maximum of and noting its sign.

So now here is what we have

was made by the substitution and was done using the continuity of the exponential function.

So now let us note something

Cutting out the uneccessary step gives us

So this implies that

Now

So we can see that

Which by the Squeeze Theorem indicates that

So then

So we can finally conclude that