Question

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

Answer 1

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

Answer 2

no, not yet.

Answer 3

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

Answer 4

\[\large\rm \lim_{x\to 0}\frac{\sin(4x)}{x \cos x}=\quad \lim_{x\to 0}\frac{\sin(4x)}{x}\cdot \lim_{x\to 0}\frac{1}{\cos x}\]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?

Answer 5

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

Answer 6

@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

Answer 7

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.

Answer 8

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

Answer 9

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

Answer 10

yay good job \c:/