Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x = a are P 1 ( x ) = f ' ( a ) ( x − a ) + f ( a ) and P 2 ( x ) = 1 2 f " ( a ) ( x − a ) 2 + f ' ( a ) ( x − a ) + f ( a ) In Exercises 55-58, (a) find the specified linear and quadratic approximations of f , and (b) use a graphing utility to graph f and the approximations. f ( x ) = arctan x , a = 0
Linear and Quadratic Approximations The linear and quadratic approximations of a function f at x = a are P 1 ( x ) = f ' ( a ) ( x − a ) + f ( a ) and P 2 ( x ) = 1 2 f " ( a ) ( x − a ) 2 + f ' ( a ) ( x − a ) + f ( a ) In Exercises 55-58, (a) find the specified linear and quadratic approximations of f , and (b) use a graphing utility to graph f and the approximations. f ( x ) = arctan x , a = 0
Solution Summary: The author explains how to find the linear and quadratic approximations of f.
Linear and Quadratic Approximations The linear and quadratic approximations of a function f at
x
=
a
are
P
1
(
x
)
=
f
'
(
a
)
(
x
−
a
)
+
f
(
a
)
and
P
2
(
x
)
=
1
2
f
"
(
a
)
(
x
−
a
)
2
+
f
'
(
a
)
(
x
−
a
)
+
f
(
a
)
In Exercises 55-58, (a) find the specified linear and quadratic approximations of f, and (b) use a graphing utility to graph f and the approximations.
Only 100% sure experts solve it correct complete solutions ok
rmine the immediate settlement for points A and B shown in
figure below knowing that Aq,-200kN/m², E-20000kN/m², u=0.5, Depth
of foundation (DF-0), thickness of layer below footing (H)=20m.
4m
B
2m
2m
A
2m
+
2m
4m
sy = f(x)
+
+
+
+
+
+
+
+
+
X
3
4
5
7
8
9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
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