Question

What is the limit as x approaches 0 of `sin^2(x) 4x`?

Answer 1

It's `0`.

This is a continuous function, which means that there isn't an `x` value for which the `y` value doesn't exist. The limit of continuous functions is simply the function value, the `y` value:

`lim_{x \to 0} sin^2(x)4x = sin^2(0)*4*0 = 0`

So the limit is equal to 0.
Take a look at the function.

Here you can also see that te answer is 0.