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Mathematics
Mathematics
Problem
For a function
f
f
f
, the graph satisfies the following near
x
=
3
x=3
x
=
3
: •
f
(
x
)
f(x)
f
(
x
)
approaches
2
2
2
as
x
→
3
−
x\to 3^{-}
x
→
3
−
. •
f
(
x
)
f(x)
f
(
x
)
approaches
8
8
8
as
x
→
3
+
x\to 3^{+}
x
→
3
+
. • The point
(
3
,
5
)
(3,5)
(
3
,
5
)
is filled on the graph. State (i)
lim
x
→
3
−
f
(
x
)
\displaystyle \lim_{x\to 3^{-}}f(x)
x
→
3
−
lim
f
(
x
)
, (ii)
lim
x
→
3
+
f
(
x
)
\displaystyle \lim_{x\to 3^{+}}f(x)
x
→
3
+
lim
f
(
x
)
, and (iii) whether
lim
x
→
3
f
(
x
)
\displaystyle \lim_{x\to 3}f(x)
x
→
3
lim
f
(
x
)
exists.
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