Question

How do you find the limit of `(e^(3x) - e^(5x))/(x)` as x approaches 0?

Answer 1

Use l'Hospital's Rule.

Explanation:

`lim_(xrarr0) (e^(3x)-e^(5x))/x` has initial form `(1-1)/0 = 0/0`.

We can apply l"Hospital's rule to try to find such a limit.

`lim_(xrarr0)(d/dx(e^(3x)-e^(5x)))/(d/dx(x)) = lim_(xrarr0)(3e^(3x)-5e^(5x))/1`

`= (3-5)/1 = -2`