calculus help

[lpaynerdh]

We are working on limits in class and I am stuck on one problem. I am not really sure why I can't figure this one out. Any help will be very appreciated. Thanks in advance. lim (cos (2theta) tan (2theta))/theta x approaches 0

 

[HallsofIvy]

An obvious point is that \(\displaystyle tan(2\theta)= \frac{sin(2\theta)}{cos(2\theta)}\) so that \(\displaystyle \frac{cos(2\theta)tan(2\theta)}{\theta}= \frac{cos(2\theta)\frac{sin(2\theta)}{cos(2\theta)}}{\theta}\)\(\displaystyle = \frac{sin(2\theta)}{\theta}\)

Now, multiply both numerator and denominator by 2:
\(\displaystyle 2\frac{sin(2\theta)}{2\theta}\).

Can you finish that?

 

[lpaynerdh]

Thanks.

Thanks for the help. If the answer is 2 then I understand it.

 

[Steven G]

We are working on limits in class and I am stuck on one problem. I am not really sure why I can't figure this one out. Any help will be very appreciated. Thanks in advance. lim (cos (2theta) tan (2theta))/theta x approaches 0

Let trig(x) be any trig function of x. Then almost always if you have lim as x->0 of trig(x)/x or lim as x->0 of x/trig(x) you want to get sinx/x or x/sinx and both of these two fractions go to 1 as x goes to 0. Can you prove that!