Question

How do you evaluate the limit `sin^3(2x)/sin^2(3x)` as x approaches `0`?

Answer 1

`0`

Explanation:

After the textbook result

`lim_(x->0)sin x/x = 1` we have

`sin^3(2x)/sin^2(3x) = (sin(2x)/(2x))^3/(sin(3x)/(3x))^2(2x)^3/(3x)^2`

then

`lim_(x->0)sin^3(2x)/sin^2(3x) = 1/1 8/9lim_(x->0) x = 0`