clara1223
  • 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
Mathematics
chestercat
  • chestercat
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anonymous
  • anonymous
have you tried graphing the equation and trying to solve it graphically yet?
clara1223
  • clara1223
no, not yet.
anonymous
  • anonymous
i would suggest that as the answer may become apparent to you when you graph it

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zepdrix
  • 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
  • clara1223
graphically it says that x is undefined at 0 but I need to prove it on paper
clara1223
  • 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
  • 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
  • zepdrix
So for the second limit, do step 1, .... and you're done with it.
clara1223
  • clara1223
ok 1/cos(0) is 1 so the overall answer is 4 correct?
zepdrix
  • zepdrix
yay good job \c:/

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