Worksheet 3.7 - Linearization & Differentials Math Worksheet
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5Calculus Maximus
WS 3.7: Linearization & Differentials
Name_________________________________________ Date________________________ Period______
Worksheet 3.7—Linearization & Differentials
Show all work. Calculator permitted. Show all set-ups and analysis. Report all answers to 3 decimals and
avoid intermediate rounding error.
Multiple Choice
x ?
x
1. What is the linearization of
f x
e
centered at at
1
x
(A)
L x
e
(B)
L x
ex
(C)
L x
e
(D)
L x
x e
(E)
L x
e x
1
2
. The tangent line to the graph of f at
x
2. Let f be the function given by
f x
x
2
x
3
2
is used to
approximate values of
f x . Which of the following is the greatest value of x for which the error
resulting from this tangent line approximation is less than 0.5 ?
(A) 2.4
(B) 2.5
(C) 2.6
(D) 2.7
(E) 2.8
f
. If the tangent line to the graph of f
3. Let f be a differentiable function such that
f
3
2
and
3
5
x
at
3
is used to find an approximation to a zero of f , that approximation is
(A) 0.4
(B) 0.5
(C) 2.6
(D) 3.4
(E) 5.5
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