## clara1223 one year ago find the limit as x approaches 0 of (sin(4x))/(x(cos(x))) a) -1 b) 0 c) 4 d) 1/4 e) does not exist

1. anonymous

have you tried graphing the equation and trying to solve it graphically yet?

2. clara1223

no, not yet.

3. anonymous

i would suggest that as the answer may become apparent to you when you graph it

4. zepdrix

$\large\rm \lim_{x\to 0}\frac{\sin(4x)}{x \cos x}=\quad \lim_{x\to 0}\frac{\sin(4x)}{x}\cdot \lim_{x\to 0}\frac{1}{\cos x}$Maybe this can help get us started. When I break them up this way, that first limit looks an awful lot like an identity doesn't it?

5. clara1223

graphically it says that x is undefined at 0 but I need to prove it on paper

6. clara1223

@zepdrix then I can pull a 4 out of the first limit and the answer is 4, I'm not sure how to get the second limit though

7. zepdrix

This is how you should think about limits in your brain: Step 1: Plug the limit value directly into the function. Step 2: If there is a problem, back up, and do some algebra. Step 3: Plug the limit directly in and check again.

8. zepdrix

So for the second limit, do step 1, .... and you're done with it.

9. clara1223

ok 1/cos(0) is 1 so the overall answer is 4 correct?

10. zepdrix

yay good job \c:/