For which real values of does the limit exist and remain finite but non-zero?

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

Problem

For which real values of

k

does the limit

\displaystyle L=\lim_{x\to\infty}\bigl(\sqrt{x^{2}+kx}-x\bigr)

exist and remain finite but non-zero? (a)

k>0

(b)

|k|<1

(c)

k\neq 0

(d)

k=0