Question

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

The answer is e^2; please explain how to get that?

Answer 1

First, separate the exponents of the first exponential:


`\lim_(h \to 0) (e^(2) e^(h) - e^(2) )/(h)`

Regroup e² on the numerator:

`\lim_(h \to 0) ( e^(2) (e^(h) - 1) )/(h)`

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


`e^(2) \lim_(h \to 0) ( e^(h) - 1)/(h)`

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

therefore:

e² · 1 = e²