# Math Help - Limits and l'hopitals rule

1. ## Limits and l'hopitals rule

I need help with:

Limit (cos3x)^5/x as x approaches 0

Should I use L'Hopital's Rule?
How do i begin to solve this?
I need help with the first few steps?

2. You should use nothing, there's no indeterminate form.

3. $\lim_{x \to 0} [\cos(3x)]^{\frac{5}{x}}$

let $y = [\cos(3x)]^{\frac{5}{x}}$

$\ln{y} = \frac{5}{x} \cdot \ln[\cos(3x)]$

$\lim_{x \to 0} \frac{5\ln[\cos(3x)]}{x}$

L'Hopital ...

$5 \lim_{x \to 0} {\frac{-3\sin(3x)}{\cos(3x)}} = 5 \cdot 0 = 0$

$\lim_{x \to 0} \, \ln{y} = 0$

so ...

$\lim_{x \to 0} \, y = e^0 = 1$

4. Ahh, that's what happens when they don't use a proper parenthesis.