For the real parameter

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

Problem

a

, consider the function

f_a(x)=\frac{(x-a)^{2}}{x^{2}-a},\qquad x\ne\pm\sqrt{a}.

For which value of

a

does

f_a

have exactly one removable discontinuity and exactly one infinite (vertical asymptote) discontinuity? (a)

a=2

(b)

a=-1

(c)

a=1

(d)

a=0