Mathematics

Problem

Let

p(x)=\dfrac{2}{(x-5)\lvert x-5\rvert}

. Which of the following correctly gives the one-sided limits of

p(x)

x

approaches

5

and classifies the discontinuity at

x=5

? a)

\displaystyle \lim_{x\to5^-}p(x)=+\infty

and

\displaystyle \lim_{x\to5^+}p(x)=+\infty

; the graph has a vertical asymptote at

x=5

b) Both one-sided limits are finite and equal; the graph has a removable discontinuity at

x=5

\displaystyle \lim_{x\to5^-}p(x)=-\infty

and

\displaystyle \lim_{x\to5^+}p(x)=+\infty

; the graph has a vertical asymptote at

x=5

\displaystyle \lim_{x\to5^-}p(x)=-\infty

and

\displaystyle \lim_{x\to5^+}p(x)=+\infty

; the graph has a jump discontinuity at

x=5