MATLAB: Can any one help to find the limit of a function f=(2-2*cos​(x))/x^3*s​in(x)-cos(​x)/x*sin(x​) where x tending 0. correct ans is -5/12 but im getting zero.

Question

Can any one help me to find the limit of a function f=(2-2*cos(x))/x^3*sin(x)-cos(x)/x*sin(x) where x tending 0. correct ans is -5/12 but i'm getting zero.

Answer 1

No, the answer is 0. You can taylor() the expression near 0 and you will see that there is no constant term, only even powers of x, so the answer must be non-negative and must approach 0 as x approaches 0.