## 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

1. zepdrix

Sines and cosines? :o Oh ok, this will be almost identical to the last problem then.

2. zepdrix

$\large\rm \lim_{x\to 0}\frac{\tan(3x)}{x}=\lim_{x\to 0}\frac{\frac{\sin(3x)}{\cos(3x)}}{x}=\lim_{x\to 0}\frac{\sin(3x)}{x \cos(3x)}$Going further,$\large\rm =\lim_{x\to 0}\frac{\sin(3x)}{x}\cdot\lim_{x\to 0}\frac{1}{\cos(3x)}$

3. zepdrix

You ok with that third equals sign? I know that little algebra step can be tricky.

4. clara1223

yes, I understand

5. clara1223

so the answer again is just 3 times 1?

6. zepdrix

yay \c:/