## Calculus 8th Edition

(a)$\lim_{x\to \infty } f(x) = -2$ (b) $\lim_{x\to- \infty } f(x) = 2$ (c)$\lim_{x\to1 } f(x) = \infty$ (d) $\lim_{x\to3 } f(x) =-\infty$ (e) $y=2$ , $y=-2$ , $x=1$ and $x=3$
(a) From the given figure , as $x \to \infty$ the graph of $f(x)$ seems to level out at $y = -2$, then $\lim_{x\to \infty } f(x) = -2$ (b) From the given figure , as $x \to -\infty$ the graph of $f(x)$ seems to level out at $y =2$, then $\lim_{x\to- \infty } f(x) = 2$ (c) From the given figure , as $x \to 1$ the graph of $f(x)$diverges towards $\infty$, then $\lim_{x\to1 } f(x) =\infty$ (d) From the given figure , as $x \to 3$ the graph of $f(x)$diverges towards $-\infty$, then $\lim_{x\to3 } f(x) =-\infty$ (e) From part (a) to (c) , the equations of asymptotes are $y=2$ , $y=-2$ , $x=1$ and $x=3$