Limit of (sin(2x))^3/(sin(3x))^3 as x Approaches 0: Solution

[Nitrate]

Homework Statement

evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3

Homework Equations

The Attempt at a Solution

the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but I'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)

 

[LCKurtz]

Homework Statement

evaluate the limit as x approaches 0 of (sin(2x))^3/(sin(3x))^3

Homework Equations

The Attempt at a Solution

the answer in the textbook is 8/27
i figured they got that by raising 2 to the 3rd and 3 to the 3rd
but I'm not entirely sure what happens to the sin's

id really appreciate a worked out answer (that doesn't use l'hopital's rule)

We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.

 

[Nitrate]

We don't do worked out answers. But here's a hint: Presumably you know something about the limit of sin(x)/x as x → 0. Make use of that by multiplying and dividing by certain powers of x.

well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question

 

[LCKurtz]

well
lim
x->0 sinx/x = 1
the problem is that i don't know how to apply it to this question

What would be the limit of \frac {\sin(2x)}{2x} as x → 0?

 

[Nitrate]

What would be the limit of \frac {\sin(2x)}{2x} as x → 0?

that limit would be 1 as well
but I'm still not sure how it'd help

 

[LCKurtz]

that limit would be 1 as well
but I'm still not sure how it'd help

Now read the hint I gave in post #2 again. Hopefully you will see it; I'm signing off for tonight.