Question

How do you find the limit of `(sin^2(x^2))/(x^4)` as x approaches 0?

Answer 1

`1`

Explanation:

Let `f(x)=(sin^2(x^2))/x^4`

`implies f'(x)=lim_(x to 0) (sin^2(x^2))/x^4`

`implies f'(x)=lim_(x to 0) (sin(x^2)*sin(x^2))/x^4=lim_(x to 0) {sin(x^2)/x^2*sin(x^2)/x^2}=lim_(x to 0)sin(x^2)/x^2lim_(x to 0)sin(x^2)/x^2*=1*1=1`