## roseflight 2 years ago What is the limit of sin(2x)/(3x) as x approaches 0

1. zordoloom

Would you like the step by step?

2. roseflight

3. TuringTest

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

4. roseflight

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

5. TuringTest

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

6. roseflight

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

7. dpaInc

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