# Thread: Does this limit exist?

1. ## Does this limit exist?

I'm supposed to calculate the limit if it exists. Can you can firm that this one doesn't exist:

limit as x approaches 0 of [1 - cos(4x)] / [9x^2]

I know that

lim as x approaches 0 of [1 - cos ax] / [ax] = 0, however, I don't think you can manipulate the above to help you.

2. $\lim_{x\rightarrow 0} \frac{1-cos(4x)}{9x^2}$

= $\lim_{x\rightarrow 0} \frac{2sin^2(2x)}{9x^2}$

= $\lim_{x\rightarrow 0} \frac{8sin^2(2x)}{9(2x)^2}$

= $\frac{8}{9}$ ( $\lim_{x\rightarrow 0} \frac{sinx}{x}=1)$