suppose f is continuous on the open interval from negative i

suppose f is continuous on the open interval from negative infinity to positive infinity and f(1)=1. I was given the hint that this problem involves using the concepts of limits, derivative, integral, L\'Hopital\'s rule, chain rule, and the fundamental theorem of calculus.

Solution

apply l\' hospital -sinx^2 * 2x*f(cosx^2)/4x^3 -sinx^2**f(cosx^2)/2x^2 put the limit -1/2