limit x-0, tan^2(x)/(x) find the limit, help me!!

Question

limit x->0, tan^2(x)/(x) find the limit, help me!!

agent0smith · Answer

Have you learned l'hopitals rule?

anonymous · Answer

yes, derivate?

agent0smith · Answer

Yeah i'd try that first, since it's indeterminate form...

anonymous · Answer

I try to do this but I can't find the solution

agent0smith · Answer

Can you differentiate tan^2x? Do it like (tanx)^2 and just use the chain rule. Derivative of the x is just 1.

anonymous · Answer

of course but the problem is in the derivative of tan^2(x)

agent0smith · Answer

(tanx)^2 is the same as tan^2x... if you can differentiate one, you can differentiate the other...

agent0smith · Answer

$$\Large \frac{ d }{ dx } f(x)^n = n f(x)^{n-1}*f \prime (x)$$

anonymous · Answer

yes I know
the result is 2tan(x)

agent0smith · Answer

Follow the chain rule i showed above... you're missing something.

anonymous · Answer

I can't find the mistake, help me please

agent0smith · Answer

Look at the chain rule... you're missing the derivative of tanx.

anonymous · Answer

sec^2x ?

agent0smith · Answer

Yes, that's what you were missing.

anonymous · Answer

and how I can to evaluate with 0 if I have sec^2x

agent0smith · Answer

You can evaluate easily. Secant is 1/cosine...

anonymous · Answer

what?

anonymous · Answer

i havee secant but sec^2

agent0smith · Answer

Yep... so you can evaluate 2tanxsec^2x for x=0.

anonymous · Answer

1/cosx is for the secant not fot sec^2

agent0smith · Answer

secx = 1/cosx

sec^2x = 1/cos^2x

agent0smith · Answer

because sec^2x = (1/cosx)^2 ... understand...?

agent0smith · Answer