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Mathematics
Mathematics
Problem
Let
g
g
g
be the function defined by
g
(
x
)
=
{
∣
x
∣
x
,
x
≠
0
2
,
x
=
0.
g(x)=\begin{cases}\dfrac{|x|}{x},&x\neq0\\2,&x=0.\end{cases}
g
(
x
)
=
⎩
⎨
⎧
x
∣
x
∣
,
2
,
x
=
0
x
=
0.
Determine
lim
x
→
0
g
(
x
)
\displaystyle\lim_{x\to0}g(x)
x
→
0
lim
g
(
x
)
, or state that the limit does not exist.
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