Let be a real number

MATHEMATICS · Subjective · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

k

be a real number. Define

F(x)=\frac{x^{2}-kx-2}{x-1},\quad x\neq 1.

(i) Determine the value of

k

for which

\displaystyle \lim_{x\to 1} F(x)

exists and equals

3

. (ii) For this value of

k

, simplify

F(x)

and write the continuous extension of

F

x=1