Question

calculate the following limits:

lim sin(2x)/sin(3x) as x approaches to 0.

Answer 1

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

Answer 2

when you do that you will simply get 2/3

Answer 3

so your limit will be 2/3

Answer 4

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

Answer 5

what calculus class are you in?

Answer 6

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

Answer 7

calculus 1. Thanks.

Answer 8

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

Answer 9

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.

Answer 10

thank you,