Answer
(a). $\infty $
(b). $-\infty $
Work Step by Step
Use the known limit, $\lim_{x\to\pm\infty}\frac{1}{x^n}=0, n=1,2,3,...$
(a) $\lim_{x\to\infty}\frac{x^3+7x^2-2}{x^2-x+1}=\lim_{x\to\infty}\frac{x+7-2/x^2}{1-1/x+1/x^2}=\infty $
(b) $\lim_{x\to-\infty}\frac{x^3+7x^2-2}{x^2-x+1}=\lim_{x\to-\infty}\frac{x+7-2/x^2}{1-1/x+1/x^2}=-\infty $
