lim (4sin2x - 3x cos5x)/(3x/2 +(x^2)cscx )

Question

x->0

Answer 1

L'Hoptial's rule applies to this.

I get for the numerator..

8cos2x - 3cos5x - 15x sin5x

and the denominator...
3/2 + 2x csc x + x^2 d cscx/dx

so the limit looks to be
5/ (3/2) = 10/3

check me.