limit as x approaches xcot2x- sin^23x/3x^2

Question

got stuck on trying to figure out cot and how to get rid of the x

Answer 1

When x is very small, tan(x)=x, so cot(2x)=1/2x, sin(x)=x so sin^2(3x)=9x^2. Assuming the question is asking for the limit as x approaches zero of xcot(2x)-sin^2(3x)/3x^2, then we have x/2x-9x^2/3x^2 which is 0.5-3=-2.5.