## Calculus: Early Transcendentals 8th Edition

(a). Evaluate each limit: (i) $\lim\limits_{x \to 1^{-}}$ $g(x) = 1$ (ii) $\lim\limits_{x \to 1}$ $g(x) = 1$ (iii) $g(1) = 3$ (iv) $\lim\limits_{x \to 2^{-}}$ $g(x) = -2$ (v) $\lim\limits_{x \to 2^{+}}$ $g(x) = -1$ (vi) $\lim\limits_{x \to 2}$ $g(x) =$ Does not exist b. Graph
(i) $\lim\limits_{x \to 1^{-}}$ $g(x)$ $\lim\limits_{x \to 1^{-}}$ $x = 1$ (ii) $\lim\limits_{x \to 1}$ $g(x)$ $\lim\limits_{x \to 1} (2-x^{2})$ $\lim\limits_{x \to 1} (2 - 1^{2}) = 1$ (iii) $g(1)$ $g(1) = 3$ (iv) $\lim\limits_{x \to 2^{-}} g(x)$ $\lim\limits_{x \to 2^{-}} (2-x^{2})$ $\lim\limits_{x \to 2^{-}} (2-2^{2}) = (2 - 4) = -2$ (v) $\lim\limits_{x \to 2^{+}} g(x)$ $\lim\limits_{x \to 2^{+}} (x-3)$ $\lim\limits_{x \to 2^{+}} (2 - 3) = -1$ (vi) $\lim\limits_{x \to 2} g(x)$ The limit does not exists because $\lim\limits_{x \to 2^{+}} g(x)$ $\ne$ $\lim\limits_{x \to 2^{-}} g(x)$