This seems to easy. Check please.

Question

Find.
Lim (x^2)-4
x->2 e

I substitute in 2
(2^2)-4
e

gives me
4-4
e

So my answer is e^0 or 1.

Answer 1

from the work that you show , I must assume you have

Lim e^(x^2 - 4) as x-> 2

= e^0 = 1

you are correct