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Mathematics
Problem
For
f
(
x
)
=
ln
x
f(x)=\ln x
f
(
x
)
=
ln
x
, calculate the average rate of change of
f
f
f
at
x
=
3
x=3
x
=
3
over each interval
[
3
,
3.2
]
[3,3.2]
[
3
,
3.2
]
,
[
3
,
3.1
]
[3,3.1]
[
3
,
3.1
]
, and
[
3
,
3.05
]
[3,3.05]
[
3
,
3.05
]
. Using the pattern you observe, state a numerical estimate (to four decimal places) for the instantaneous rate of change of
f
f
f
at
x
=
3
x=3
x
=
3
.
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