First, separate the exponents of the first exponential:
[tex] \lim_{h \to 0} \frac{e^{2} e^{h} - e^{2} }{h} [/tex]
Regroup e² on the numerator:
[tex] \lim_{h \to 0} \frac{ e^{2} (e^{h} - 1) }{h} [/tex]
e² is now a constant that can be brought outside the limit:
[tex] e^{2} \lim_{h \to 0} \frac{ e^{h} - 1}{h}
[/tex]
This limit is a notable one, and we know it is equal to 1,
therefore:
e² · 1 = e²
