The limit as h approaches 0 of (e^ (2+h) - e^2) / h is?

If you plug in 0, you get the indeterminate form 0/0. You can, therefore, apply L'Hopital's Rule to get the limit as h approaches 0 of e^ (2+h),

which is just e^2.

[e^ (2+h) - e^2] / h = [ e^2 (e^h - 1) ] / h

so in the limit, as h goes to 0, you'll notice that the numerator and denominator each go to zero (e^h goes to 1, and so e^h-1 goes to zero). This means the form is 'indeterminate' (here, 0/0), so we may use L'Hoptial's rule:

= e^2