a: \(=\lim\limits_{x\rightarrow2}\dfrac{x^4-4x^2+x^2-4}{x^3-2x^2-x^2+2x+2x-4}\)
\(=\lim\limits_{x\rightarrow2}\dfrac{x^2\left(x-2\right)\left(x+2\right)+\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x^2-x+2\right)}\)
\(=\lim\limits_{x\rightarrow2}\dfrac{\left(x+2\right)\left(x^2+1\right)}{x^2-x+2}=\dfrac{4\left(2^2+1\right)}{2^2-2+2}=5\)
b: \(=\lim\limits_{x\rightarrow-\infty}\left[x\cdot\dfrac{x^2-2-x^2-2}{\sqrt{x^2-2}+\sqrt{x^2+2}}\right]\)
\(=\lim\limits_{x\rightarrow-\infty}\left(x\cdot\dfrac{-4}{\sqrt{x^2-2}+\sqrt{x^2+2}}\right)\)
\(=\lim\limits_{x\rightarrow-\infty}\left(x\cdot\dfrac{-4}{x\left(\sqrt{1-\dfrac{2}{x^2}}+\sqrt{1+\dfrac{2}{x^2}}\right)}\right)\)
\(=\lim\limits_{x\rightarrow-\infty}\left(\dfrac{-4}{\sqrt{1-\dfrac{2}{x^2}}+\sqrt{1+\dfrac{2}{x^2}}}\right)\)
\(=\dfrac{-4}{1+1}=\dfrac{-4}{2}=-2\)
