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Mathematics
Mathematics
Problem
Let
f
f
f
be the function defined by
f
(
x
)
=
{
3
x
+
k
,
x
<
2
,
k
x
2
−
8
,
x
≥
2.
f(x)= \begin{cases} 3x+k, & x<2,\\ kx^{2}-8, & x\ge 2. \end{cases}
f
(
x
)
=
{
3
x
+
k
,
k
x
2
−
8
,
x
<
2
,
x
≥
2.
Determine the value of
k
k
k
for which
lim
x
→
2
f
(
x
)
\displaystyle\lim_{x\to 2} f(x)
x
→
2
lim
f
(
x
)
exists.
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