## Calculus: Early Transcendentals 8th Edition

(a) $\lim\limits_{x \to \infty}f(x) = 0$ (b) $\lim\limits_{x \to 0^+}f(x) = \infty$ (c) $\lim\limits_{x \to 1^-}f(x) = \infty$ (d) $\lim\limits_{x \to 1^-}f(x) = -\infty$ (e) We can see a sketch of the graph below.
$f(x) = \frac{2}{x} - \frac{1}{ln~x}$ (a) As $~~x \to \infty~~$, the value of $\frac{2}{x}$ approaches $0$ while $\frac{1}{ln~x}$ approaches $0$ $\lim\limits_{x \to \infty}f(x) = 0$ (b) As $~~x \to 0^+~~$, the value of $\frac{2}{x}$ approaches $\infty$ while $\frac{1}{ln~x}$ approaches $0$ $\lim\limits_{x \to 0^+}f(x) = \infty$ (c) As $~~x \to 1^-~~$, the value of $\frac{2}{x}$ approaches $2$ while $\frac{1}{ln~x}$ approaches $-\infty$ $\lim\limits_{x \to 1^-}f(x) = \infty$ (d) As $~~x \to 1^+~~$, the value of $\frac{2}{x}$ approaches $2$ while $\frac{1}{ln~x}$ approaches $\infty$ $\lim\limits_{x \to 1^-}f(x) = -\infty$ (e) We can see a sketch of the graph below.