Worksheet 2.10 Derivatives Of Log Functions & Log Diff Page 7
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7Calculus Maximus
WS 2.10: Log Functions
(
)
(
)
⎡
+
−
+
⎤
_____ 15. Determine if
lim ln 2 5
x
ln 2 3
x
⎦ exists, and if it does, find its value.
⎣
→∞
x
1
(A)
ln
2
5
(B)
ln
3
3
(C)
ln
5
(D) ln 2
(E) Does Not Exist
2ln
t
( )
=
_____ 16. Find the derivative of
f t
.
+
3 ln
t
2
( )
′
=
(A)
f t
(
)
2
+
t
3 ln
t
6ln
t
( )
′
=
(B)
f t
(
)
2
+
3 ln
t
6
( )
′
=
(C)
f t
(
)
2
+
3 ln
t
2
( )
′
=
(D)
f t
(
)
+
t
3 ln
t
6
( )
′
=
(E)
f t
(
)
2
+
t
3 ln
t
( )
4x
=
_____ 17. Determine the derivative of f when
f x
x
( ) (
)
4
x
′
=
+
(A)
f x
ln
x
4
x
( )
(
)
4
x
′
=
+
(B)
f x
4 ln
x
1
x
( )
(
)
′
=
+
(C)
f x
4 ln
x
1
( ) (
)
4
x
′
=
+
(D)
f x
ln
x
1
x
(
)
( )
−
4
x
1
′
=
(E)
f x
4
x
( )
(
)
(
)
=
⎡
+
⎤
_____ 18. Find the derivative of f when
f x
x
7sin ln
x
2cos ln
x
⎦ .
⎣
( )
(
)
(
)
′
=
⎡
+
⎤
(A)
f x
x
5sin ln
x
9cos ln
x
⎣
⎦
( )
(
)
(
)
′
=
−
(B)
f x
5sin ln
x
9cos ln
x
( )
(
)
(
)
′
=
+
(C)
f x
5sin ln
x
9cos ln
x
( )
(
)
(
)
′
=
+
(D)
f x
9sin ln
x
5cos ln
x
( )
(
)
(
)
′
=
⎡
+
⎤
(E)
f x
x
9sin ln
x
5cos ln
x
⎣
⎦
Page 7 of 7
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