How do I solve the limit of tan^2(2x) / 3x^2 as x approaches 0?

[theCandyman]

I am completely lost on where to start, any help would be appreciated:

lim (x->0) tan^2(2x) / 3x^2

I do not have any work so far, but I'm trying to find a way to get rid of the x^2 in the denominator, which so far has been fruitless.

 

[shmoe]

Try replacing tan(2x) with sin(2x)/cos(2x). You probably know something about the limit of sin(x)/x as x->0.

 

[dextercioby]

I am completely lost on where to start, any help would be appreciated:

lim (x->0) tan^2(2x) / 3x^2

I do not have any work so far, but I'm trying to find a way to get rid of the x^2 in the denominator, which so far has been fruitless.

This limit works fine without the aid of Mr.L'Ho^pital.
Are u 100% convinced that:
$$\lim_{2x \rightarrow 0} \frac{\tan{2x}}{2x} =1$$
??

If so,u'll be able to apply the formula above properly and get the result.

One more hint:
$$\lim_{x \rightarrow 0} \frac{\tan^{2} 2x}{3x^2} = \frac{4}{3} (\lim_{2x \rightarrow 0} \frac{\tan{2x}}{2x})^{2}$$

I hope you can take it from there.

 

[theCandyman]

Thank you both, I have my answer now.