Question

How do you find the limit of `(sinx(1-cosx))/(2x^2)` as `x->0`?

Answer 1

`lim_(x->0) (sinx(1-cosx))/(2x^2) = 0`

Explanation:

We know that:

`lim_(x->0) sinx/x = 1`

and:

`lim_(x->0) (1-cosx)/x = 0`

So:

`lim_(x->0) (sinx(1-cosx))/(2x^2) = 1/2 lim_(x->0) (sinx/x )((1-cosx)/x) = 1/2 xx 1 xx 0 = 0`