Trigonometric limit question, see comment for equation.

Question

anonymous · Answer

$$\lim_{\theta \rightarrow 0}(2t)/(sint-t)$$

turingtest · Answer

can we use calculus?
L'hospital's rule?

anonymous · Answer

I believe so.

turingtest · Answer

L'hospital's rule once
then evaluate
got it?

anonymous · Answer

I've been attempting to solve it and so far have only been able to factor out the "t" in the denominator, from there I am unable to figure out the next step.

turingtest · Answer

do you know L'hospital's rule?

anonymous · Answer

No, I don't believe I fully understand it. It doesn't look like anything that I have learned in class so far.

turingtest · Answer

are you in calc or precalc?

anonymous · Answer

calc

turingtest · Answer

then you should use L'hospitals rule:
when yuo have a limit that evaluates to 0/0 or infty/infty, take the derivative of the top and bottom, then see if you can take the limit again.
That is L'hospital's rule.
Want a demonstration for this problem?

turingtest · Answer

or do you want to try it yourself?

anonymous · Answer

Oh, ok I see now, we have been learning this just the name was unfamiliar. Right now it's the deriving that I'm getting stuck on so an example would be great.

anonymous · Answer

I've got to go now, but you've been a great help. Thanks for clearing that up for me I appreciate it.

turingtest · Answer

no time for the example?
ok then good luck!

turingtest · Answer

for future reference$$\lim_{t \rightarrow 0}\frac{2t}{\sin t-t}=\lim_{t \rightarrow 0}\frac{2}{\cos t-1}=-\infty$$