A limit problem: Lim as X-->0 of (tan^2 X)/X

[Ken]

I'm struggling with the following problem:

Lim as X-->0 of (tan^2 X)/X


Thanks

 

[pka]

Take note that:
\(\displaystyle \L
\frac{{\tan ^2 (x)}}{x} = \left( {\frac{{\sin (x)}}{x}} \right)\left( {\frac{1}{{\cos ^2 (x)}}} \right)\left( {\sin (x)} \right).\)

 

[galactus]

You can break it up into fractions:

\(\displaystyle \L\\\lim_{x\to\0}\frac{tan^{2}(x)}{x}=\lim_{x\to\0}\frac{sin(x)}{x}\cdot\lim_{x\to\0}\frac{sin(x)}{1}\cdot\lim_{x\to\0}\frac{1}{cos^{2}(x)}\)

You should see a familiar limit in sin(x)/x.

 

[Ken]

A limit problem

Thank you for your help. I need to digest your responses a bit.

 

[galactus]

You just need to remember the classic identity \(\displaystyle \L\\\frac{sin(x)}{cos(x)}=tan(x)\). That's all it is.