# Evaluate the following limit: $\lim \limits_{x\to+\infty}\frac{(3^x+x^3)\sin(x)}{(3^x + x^2)}$

I'm having big problem evaluating the next limit:

$$\lim_{x\to+\infty}\frac{(3^x+x^3)\sin(x)}{(3^x + x^2)}$$

The limit does not exist since: $$\lim_{x \to +\infty}\frac{3^x+x^3}{3^x+x^2}=1$$ but $\lim_{x \to +\infty}\sin x$ does not exist.