Let . Which one of the following statements about is…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

F(x)=\dfrac{(x-2)^{3}(x+1)}{(x-2)^{2}(x-5)}

. Which one of the following statements about

F

is correct? (a)

F

is continuous at

x=2

and has a vertical asymptote at

x=5

. (b)

F

has vertical asymptotes at both

x=2

and

x=5

. (c)

F

has a removable discontinuity at

x=2

and a vertical asymptote at

x=5

. (d)

F

has removable discontinuities at both

x=2

and

x=5