# evaluating limits with trig functions

• February 8th 2009, 09:10 PM
calcbeg
evaluating limits with trig functions
Hi

I am on my last question so hopefully someone is still out there to help me!

Question says "evaluate the following limits"

First

lim x/tan x
x->0

Second

lim x2/(1-cos^2 x)
x_>0

I can't seem to find any examples of how to do either of these.

$\lim_{x\to 0}\frac{x}{\tan x}=\lim_{x\to 0}\underbrace{\frac{x}{\sin x}}_{\to 1}\underbrace{\cos x}_{\to 1}=1.$
$\lim_{x\to 0}\frac{x^2}{1-\cos^2 x}=\lim_{x\to 0}\frac{x^2}{\sin^2 x}=\lim_{x\to 0}\left(\frac{x}{\sin x}\right)^2=1^2=1.$