Explanation

To evaluate the limit, we can start by rewriting the expression as:

lim (sin(2x) + a*sin(x)) / x^3

As x approaches 0, the sine functions can be approximated by their arguments, so we get:

lim (2x + a*x) / x^3 = lim (2 + a) / x^2

For this limit to exist, the numerator must be 0, so we set 2 + a = 0, which gives a = -2.