Question #b82b5

1 Answer
Dec 23, 2017

Infinity

Explanation:

realize that 1 - cos^2 x = sin^2 x 1cos2x=sin2x due to the trigonometric identity sin^2 x + cos^2 x = 1 sin2x+cos2x=1

therefore the top equation becomes sin(x) * x^2 * sin(x)sin(x)x2sin(x) which is equal to x^2 * sin^2 (x)x2sin2(x), after removing the common factors x^2x2 of the denominator and the numerator, you are left with sin^2 (x) / x^4sin2(x)x4

the sin^2sin2 function has its domain over only 1 and 0 so it will never be negative or more than that and the bottom function x^4x4 gets smaller and smaller as xx approaches 00, 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 xx approaches 0 is positive Infinity