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Mathematics
Mathematics
Problem
For the function
f
(
x
)
=
{
⌊
x
⌋
,
x
<
2
,
x
,
x
≥
2
,
f(x)=\begin{cases}\lfloor x\rfloor,& x<2,\\x,& x\ge 2,\end{cases}
f
(
x
)
=
{
⌊
x
⌋
,
x
,
x
<
2
,
x
≥
2
,
where
⌊
x
⌋
\lfloor x\rfloor
⌊
x
⌋
denotes the greatest integer less than or equal to
x
x
x
, find the left-hand limit and the right-hand limit of
f
(
x
)
f(x)
f
(
x
)
as
x
→
2
x\to 2
x
→
2
.
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