Question

find the value of c if the limit of x^2+cx+4devided by x-5 exists as x approaches 5

Answer 1

Take
\[c= -\frac {29}4
\]
and notice that
\[x^2-\frac{29 x}{5}+4
=\frac{1}{5} (x-5) (5 x-4)
\]
\[
\frac {\frac{1}{5} (x-5) (5 x-4)} {x-5}=
\frac 1 5 (5x-4)

\]
which tends to
\[ \frac {21}5\] when x tend to 5

Answer 2

Try to figure out, how one can find
\[ c= - \frac {29}4\]