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anonymous
 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
anonymous
 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

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0have you tried graphing the equation and trying to solve it graphically yet?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i would suggest that as the answer may become apparent to you when you graph it

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.1\[\large\rm \lim_{x\to 0}\frac{\sin(4x)}{x \cos x}=\quad \lim_{x\to 0}\frac{\sin(4x)}{x}\cdot \lim_{x\to 0}\frac{1}{\cos x}\]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?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0graphically it says that x is undefined at 0 but I need to prove it on paper

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@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
 one year ago
Best ResponseYou've already chosen the best response.1This 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
 one year ago
Best ResponseYou've already chosen the best response.1So for the second limit, do step 1, .... and you're done with it.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok 1/cos(0) is 1 so the overall answer is 4 correct?
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