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5. Applications of Derivatives
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Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
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Problem 14
Problem 15
5. Applications of Derivatives
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5. Applications of Derivatives / Linearization / Problem 9
Problem 9
Find the linear approximation of the function
g
(
x
)
g(x)
g
(
x
)
for small values of
x
x
x
using the formula
(
1
+
x
)
k
≈
1
+
k
x
(1 + x)^k ≈ 1 + kx
(
1
+
x
)
k
≈
1
+
k
x
.
g
(
x
)
=
(
1
+
x
)
4
g(x)=(1+x)^4
g
(
x
)
=
(
1
+
x
)
4
A
1
+
4
x
1+4x
B
1
+
2
x
1+2x
C
4
+
x
4+x
D
3
+
x
3+x
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