Question

What is the limit of `(sin2x)/(sin3x)` as x approaches 0?

Answer 1

`Lt_(x->0)(sin2x)/(sin3x)=2/3`

Explanation:

As `Lt_(t->0)sintheta/theta=1` ............(1)

`Lt_(x->0)(sin2x)/(sin3x)`

= `Lt_(x->0)((sin2x)/(2x))/((sin3x)/(3x))xx(2x)/(3x)`

= `(Lt_(2x->0)((sin2x)/(2x)))/(Lt_(3x->0)((sin3x)/(3x)))xx2/3`

= `1/1xx2/3` - using (1)

= `2/3`