University Calculus: Early Transcendentals (3rd Edition)

(a) $\lim_{x\to2}f(x)=0$ (b) $\lim_{x\to-3^+}f(x)=-2$ (c) $\lim_{x\to-3^-}f(x)=2$ (d) $\lim_{x\to-3}f(x)$ does not exist (e) $\lim_{x\to0^+}f(x)=-1$ (f) $\lim_{x\to0^-}f(x)=\infty$ (g) $\lim_{x\to0}f(x)$ does not exist (h) $\lim_{x\to\infty}f(x)=1$ (i) $\lim_{x\to-\infty}f(x)=0$
(a) $\lim_{x\to2}f(x)=0$ As $x$ approaches $2$, $f(x)$ approaches $0$ from both the left and the right side. (b) $\lim_{x\to-3^+}f(x)=-2$ As $x$ approaches $-3$ from the right, $f(x)$ approaches $-2$. (c) $\lim_{x\to-3^-}f(x)=2$ As $x$ approaches $-3$ from the left, $f(x)$ approaches $2$. (d) $\lim_{x\to-3}f(x)$ does not exist Since $\lim_{x\to-3^-}f(x)\ne\lim_{x\to-3^+}f(x)$, there is no single value that $f(x)$ would approach as $x\to-3$. (e) $\lim_{x\to0^+}f(x)=-1$ As $x$ approaches $0$ from the right, $f(x)$ approaches $-1$. (f) $\lim_{x\to0^-}f(x)=\infty$ As $x$ approaches $0$ from the left, $f(x)$ gets infinitely large, so we can say $f(x)$ approaches $\infty$. (g) $\lim_{x\to0}f(x)$ does not exist Since $\lim_{x\to0^-}f(x)\ne\lim_{x\to0^+}f(x)$, there is no single value that $f(x)$ would approach as $x\to0$. (h) $\lim_{x\to\infty}f(x)=1$ As $x$ gets infinitely large, or approaches $\infty$, $f(x)$ approaches $1$. (i) $\lim_{x\to-\infty}f(x)=0$ As $x$ gets infinitely small, or approaches $-\infty$, $f(x)$ approaches $0$.