Mathematics

Problem

Let

F(x)=\dfrac{x^{2}+kx+1}{2x+5}

, where

k

is a real parameter. Examine the following questions concerning the limit of

F

x

approaches

-2

. a. (i) Show that

\displaystyle \lim_{x\to -2}F(x)

exists for all real values of

k

and obtain the limit in terms of

k

." b. (ii) Determine the numerical value of this limit when

k=4

." c. (iii) Does the value of

k

affect the continuity of

F

x=-2

? Give a brief justification."