## 6.5. Differentiable Functions

### Examples 6.5.16(c):

First, we need to write this expression as a fraction before we can try to apply l'Hospital's rule:Written in this form we see that we can apply l'Hospital's rule. It leads to the expression

This is again an expression for which l'Hospital's rule applies. We get the expression

For this expression we get that the limit as x approaches zero is zero. Hence, according to l'Hospital's rule applied twice we get

= 0