Question #b82b5

1 Answer
Dec 23, 2017

Infinity

Explanation:

realize that 1cos2x=sin2x due to the trigonometric identity sin2x+cos2x=1

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

the sin2 function has its domain over only 1 and 0 so it will never be negative or more than that and the bottom function x4 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