A quadratic polynomial is given by

MATHEMATICS · Multi-part · CBSE · Mathematics · Limits and Derivatives · Limits and Derivatives

Problem

q(x)=k x^{2}+(k-2)x+1

, where

k

is a real parameter. (i) Find

\displaystyle \lim_{x\to3} q(x)

in terms of

k

. (ii) Determine the value of

k

for which the limit found in part (i) equals

16

. (iii) For the value of

k

obtained in part (ii), state the value of

q(3)

and comment on the relation between the limit and the function value at

x=3