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Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
{
x
2
−
4
x
−
2
,
x
<
2
,
a
x
+
1
,
x
≥
2.
f(x)=\begin{cases} \dfrac{x^{2}-4}{x-2}, & x<2,\\ ax+1, & x\ge 2. \end{cases}
f
(
x
)
=
⎩
⎨
⎧
x
−
2
x
2
−
4
,
a
x
+
1
,
x
<
2
,
x
≥
2.
For which value of
a
a
a
does
lim
x
→
2
f
(
x
)
\displaystyle \lim_{x\to2} f(x)
x
→
2
lim
f
(
x
)
exist? a)
2
2
2
b)
1
1
1
c)
1.5
1.5
1.5
d) There is no such value of
a
a
a
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