What is lim_(x->0) sin(sin3x)/(sin 7x) ?

1 Answer
Sep 22, 2017

3/7

Explanation:

My first impression is that:

lim_(x->0) sin(sin3x)/(sin 7x) = 3/7

since sin theta behaves like theta for small values of theta.

Let us start by assuming:

lim_(t->0) sin t / t = 1

Then:

lim_(x->0) sin(sin3x)/(sin7x)

= lim_(x->0) (sin(sin3x)/(sin3x) * (sin3x)/(3x) * (7x)/(sin 7x)) * 3/7

= 1 * 1 * 1 * 3/7

= 3/7