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anonymous
 one year ago
find the limit as x approaches 0 of (tan(3x))/x (Hint: write tangent in terms of sine and cosine)
a) 1/3
b) 3
c) 0
d) 1
e) does not exist
anonymous
 one year ago
find the limit as x approaches 0 of (tan(3x))/x (Hint: write tangent in terms of sine and cosine) a) 1/3 b) 3 c) 0 d) 1 e) does not exist

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zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2Sines and cosines? :o Oh ok, this will be almost identical to the last problem then.

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2\[\large\rm \lim_{x\to 0}\frac{\tan(3x)}{x}=\lim_{x\to 0}\frac{\frac{\sin(3x)}{\cos(3x)}}{x}=\lim_{x\to 0}\frac{\sin(3x)}{x \cos(3x)}\]Going further,\[\large\rm =\lim_{x\to 0}\frac{\sin(3x)}{x}\cdot\lim_{x\to 0}\frac{1}{\cos(3x)}\]

zepdrix
 one year ago
Best ResponseYou've already chosen the best response.2You ok with that third equals sign? I know that little algebra step can be tricky.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so the answer again is just 3 times 1?
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