Question

What is the limit of sin(2x)/(3x) as x approaches 0

Answer 1

Would you like the step by step?

Answer 2

Yes please

Answer 3

\[\frac{\sin(2x)}{3x}=\frac13\cdot\frac{\sin(2x)}x=\frac23\cdot\frac{\sin(2x)}{2x}\]

Answer 4

Sorry, but I still don't get how that would equal 2/3.

Answer 5

did you know that\[\lim_{x\to0}\frac{\sin x}x=1\]?

Answer 6

Haha I didn't remember that for some reason. Thanks!

Answer 7

how 'bout this then....
\(\large \frac{sin(2x)}{3x}=\frac{2sinxcosx}{3x}=\frac{2}{3}\cdot \frac{sinx}{x}\cdot cosx \)