Let , where is a real parameter. Solve the…

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Let

f(x)=(k^{2}+1)x^{3}-4kx+5

, where

k

is a real parameter. Solve the following. (i) Find

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

in terms of

k

. (ii) Determine the value of

k

for which

\displaystyle \lim_{x\to 1} f(x)=0

. Explain your steps briefly.