Find the following limit if it exists.
\lim\limits_{x \to -2}\dfrac{3+2x}{4^x}
\lim\limits_{x \rightarrow 1} \dfrac{6x - 1}{x^3 - 1}
\lim\limits_{x \rightarrow -1} \dfrac{x^2 + 2x}{x^5 - 1}
\lim\limits_{x \rightarrow 3} \dfrac{3x^2 + x + 1}{6x^2 + 2x}
\lim\limits_{x \rightarrow -2} \dfrac{3^x}{x^3}
\lim\limits_{x \rightarrow 4} \dfrac{2x - 1}{x^2 - 3^{x-2}}
\lim\limits_{x \rightarrow 3} \dfrac{5^x}{-2x^2 + 4x + 1}