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Mathematics
Mathematics
Problem
Let
g
g
g
be the function
g
(
x
)
=
{
x
2
−
1
x
−
1
,
x
<
1
,
a
x
+
1
,
x
≥
1.
g(x)= \begin{cases} \dfrac{x^{2}-1}{x-1}, & x<1,\\ a x+1, & x\ge 1. \end{cases}
g
(
x
)
=
⎩
⎨
⎧
x
−
1
x
2
−
1
,
a
x
+
1
,
x
<
1
,
x
≥
1.
Determine the value of
a
a
a
that guarantees
lim
x
→
1
g
(
x
)
\displaystyle\lim_{x\to 1} g(x)
x
→
1
lim
g
(
x
)
exists.
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