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clara1223

  • 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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  1. zepdrix
    • one year ago
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    Sines and cosines? :o Oh ok, this will be almost identical to the last problem then.

  2. zepdrix
    • one year ago
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    \[\large\rm \lim_{x\to 0}\frac{\tan(3x)}{x}=\lim_{x\to 0}\frac{\frac{\sin(3x)}{\cos(3x)}}{x}=\lim_{x\to 0}\frac{\sin(3x)}{x \cos(3x)}\]Going further,\[\large\rm =\lim_{x\to 0}\frac{\sin(3x)}{x}\cdot\lim_{x\to 0}\frac{1}{\cos(3x)}\]

  3. zepdrix
    • one year ago
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    You ok with that third equals sign? I know that little algebra step can be tricky.

  4. clara1223
    • one year ago
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    yes, I understand

  5. clara1223
    • one year ago
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    so the answer again is just 3 times 1?

  6. zepdrix
    • one year ago
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    yay \c:/

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spraguer (Moderator)
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