Mathematics

Problem

Let

p(x)=\dfrac{x+2}{x^{3}-4x}

, where

p

is defined for all

x

in its domain. Which statement correctly describes the locations of the vertical asymptotes of

p

and the corresponding one-sided limits? a) Vertical asymptotes at

x=0

and

x=2

;

p(x)\to -\infty

x\to 0^{-},\,2^{+}

and

p(x)\to +\infty

x\to 0^{+},\,2^{-}

. b) Vertical asymptotes at

x=0

and

x=2

;

p(x)\to +\infty

x\to 0^{-},\,2^{+}

and

p(x)\to -\infty

x\to 0^{+},\,2^{-}

. c) Vertical asymptotes at

x=-2,\,0,\,2

;

p(x)\to +\infty

on the right of each asymptote and

-\infty

on the left. d) Vertical asymptotes at

x=0

and

x=2

;

p(x)\to +\infty

on both sides of each asymptote.