Find the limit!!!!!!!!!!

Question

lim      sin3x sin5x/x^2

x->0

Answer 1

Given that lim(x->0) (sin(3x)sin(5x))/x^2

              = lim(x->0) (5*3)(sin(3x)sin(5x)) / [(5x)(3x)]    [Multiply by 5*3 on numerator and denominator]

             = lim(x->0) 15[sin(3x)/(3x)][sin(5x)/(5x)]

             = 15 lim(x->0) sin(3x)/(3x) lim(x->0) sin(5x)/(5x)

             = 15 lim(y->0) siny/y lim(z->0) sinz/z               [Assume y = 3x and z = 5x]

             = 15(1)(1)                                                       [Since lim(x->0) sinx/x = 1]

            = 15

Therefore lim(x->0) (sin(3x)sin(5x))/x^2 = 15.

Answer 2

Solution to the problem is