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- clara1223

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

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- clara1223

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

- chestercat

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- anonymous

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

- clara1223

no, not yet.

- anonymous

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

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- 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?

- clara1223

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

- 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

- 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.

- zepdrix

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

- clara1223

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

- zepdrix

yay good job \c:/

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