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$a/ \lim_{x \to 2} (x^3-x+5)=2^3-2+5=11\\ b/\lim_{x \to +\infty} (\sqrt{x^2+x+1}-x)\\ =\lim_{x \to +\infty} x\left(\sqrt{1+\dfrac{1}{x}+\dfrac{1}{x^2}}-1\right)\\ x \to +\infty;\sqrt{1+\dfrac{1}{x}+\dfrac{1}{x^2}}-1 \to 0\\ \Rightarrow \lim_{x \to +\infty} x\left(\sqrt{1+\dfrac{1}{x}+\dfrac{1}{x^2}}-1\right)=0\\ c)\lim \dfrac{7n^3+3n^2+2}{2n^3-2n^2}\\ =\lim \dfrac{7+\dfrac{3}{n}+\dfrac{2}{n^3}}{2-\dfrac{2}{n}}\\ =\dfrac{7}{2}\\ d)\lim_{x \to 2} \dfrac{\sqrt{x+2}-2}{2-x}\\ =\lim_{x \to 2} \dfrac{(\sqrt{x+2}-2)(\sqrt{x+2}+2)}{(2-x)(\sqrt{x+2}+2)}\\ =\lim_{x \to 2} \dfrac{x-2}{(2-x)(\sqrt{x+2}+2)}\\ =\lim_{x \to 2} \dfrac{-1}{\sqrt{x+2}+2}\\ =\lim_{x \to 2} \dfrac{-1}{\sqrt{2+2}+2}\\ =\dfrac{-1}{4}$