## ujuge321 3 years ago calculate the following limits: lim sin(2x)/sin(3x) as x approaches to 0.

1. Outkast3r09

use lhopitals rule which is $\frac{\frac{d}{dx}[\sin(2x)]}{\frac{d}{dx}[\sin(3x)]}$

2. Outkast3r09

when you do that you will simply get 2/3

3. Outkast3r09

so your limit will be 2/3

4. ujuge321

show me the process. i never learned that in class.

5. Outkast3r09

what calculus class are you in?

6. raheen

using le'hopital rule ==> lim 3co(2x)/3cos(3x) = 2/3

7. ujuge321

calculus 1. Thanks.

8. raheen

using le'hopital rule ==> lim 3cos(2x)/3cos(3x) = 2/3

9. JamesJ

If you don't yet know l'Hopitals rule, I assume you do know already that the limit as x --> 0 of (sin x) / x is 1. Now write$\frac{\sin 2x }{\sin 3x} = \frac{2}{3} \frac{\sin 2x/(2x)}{\sin 3x/(3x)}$ Then you observe that the limits of the ratios of sin over x are all 1 and hence the answer is 2/3.

10. ujuge321

thank you,