Find the following limits if they exist.
\lim\limits_{x \to -1} 4^x+3x^2
\lim\limits_{x \rightarrow 2} 4x^3 + \dfrac{2}{x}
\lim\limits_{x \rightarrow 3} x^{-2} + x^{2}
\lim\limits_{x \rightarrow \infty } \dfrac{3x}{2x^2} + \dfrac{2x}{3}
\lim\limits_{x \rightarrow 4} \dfrac{5x}{4 - x} + 16x^2 - 4x
\lim\limits_{x \rightarrow \infty } 3^{-x} + \dfrac{2x - 1}{4x^2}
\lim\limits_{x \rightarrow -3} \dfrac{2x}{3^x} + 4x^2