Question #b82b5

1 Answer
dhruv ahlawat
Dec 23, 2017

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

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