Math Help - Limit Problem

1. Limit Problem

We are working on indeterminates. The problem is finding the limit (x-tanx)/x^3 as x approaches 0. We have been using L'Hopital's so I'd assume that's the key. The calculator indicates a limit of infinity but I can't show it. Can anybody help me figure out how to do it?

2. The limit is $- \frac{1}{3}$

$\lim_{x \to 0} \frac{ x - \tan x}{x^3} = \lim_{x \to 0} \frac{ 1 - \sec^{2} x}{3x^{2}} = \lim_{x \to 0} \frac{ -2 \tan x \sec^{2} x}{6x}=$ $\lim_{x \to 0} \frac{-2 \sec^{4} x - 4 \tan^{2} x \sec^{2} x}{6} = -\frac{2}{6} = -\frac {1}{3}$

3. Ah I see! Thank you!