find the limit as x approaches 0 from the right

Question

the limit as x approaches 0 from the right (0⁺) for sqrt(x²+x)sin(x)

Answer 1

lim x→0⁺ √x² + x/sinx = lim →0⁺1/2(x² + x)^-1/2(2x + 1)/cosx = ∞ (DNE)

lim x→0⁺ √x² + x·sinx = 0·0 = 0

Answer 2

When I look at this limit, I see the limit of the product of two functions. Do you know what to do with the limit of each of those functions?