Question

Question #b82b5

Answer 1

Infinity

Explanation:

realize that `1 - cos^2 x = sin^2 x` due to the trigonometric identity `sin^2 x + cos^2 x = 1`

therefore the top equation becomes `sin(x) * x^2 * sin(x)` which is equal to `x^2 * sin^2 (x)`, after removing the common factors `x^2` of the denominator and the numerator, you are left with `sin^2 (x) / x^4`

the `sin^2` function has its domain over only 1 and 0 so it will never be negative or more than that and the bottom function `x^4` gets smaller and smaller as `x` approaches `0`, so the top function which is a number between 0 and 1 is divided by an increasingly small number, so the limit of the whole function as `x` approaches 0 is positive Infinity