The function depends on a real parameter

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

Problem

The function

g(x)=\dfrac{(k-3)x^{2}+4x-1}{(k+1)x^{2}-7}

depends on a real parameter

k

. (a) Find the value of

k

for which

\displaystyle \lim_{x \to \infty} g(x)

exists and is equal to

\dfrac{1}{2}

. Show all necessary steps. (b) For the value of

k

obtained in part (a), determine

\displaystyle \lim_{x \to -\infty} g(x)

. State your answer clearly.