Question

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

Answer 1

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

Answer 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,\[\large\rm =\lim_{x\to 0}\frac{\sin(3x)}{x}\cdot\lim_{x\to 0}\frac{1}{\cos(3x)}\]

Answer 3

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

Answer 4

yes, I understand

Answer 5

so the answer again is just 3 times 1?

Answer 6

yay \c:/