For A I know how to find the limit using (f(x+h)-f(x))/h but I know there was an easier way to find it using the derivative and the derivative i got was
{[-x^3+x]/[(x^3-4x)^2(3x^2-4)]} + (3x-1)/(x^3-4x)
but I dont know where to go.

Also for D I'm not certain but i think if f(x)=f(-x) its even
and if -f(x)=f(-x) its odd?