Question

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

Answer 1

First, separate the exponents of the first exponential:

$\lim_{h \to 0} \frac{e^{2} e^{h} - e^{2} }{h}$

Regroup e² on the numerator:
$\lim_{h \to 0} \frac{ e^{2} (e^{h} - 1) }{h}$

e² is now a constant that can be brought outside the limit:

$e^{2} \lim_{h \to 0} \frac{ e^{h} - 1}{h}$

This limit is a notable one, and we know it is equal to 1,

therefore:

e² · 1 = e²