Sample nal+2+A2Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curvesabout the given lines.11) y = 4 - x2,SLCnsviay= 4,x 2; revolve about the line y = 411)Solve the initial value problem.d3yIcregmbib bJ5thobudgic 12)12)dx39: y" (0) 3, y'(0) 4, y(0) 5f(b) f(a)Find the value or values of c that satisfy the equationf'(c) in the conclusion of the Mean Value Theoreb - ahe function and interval.or13)13) f(x) = x2+ 3x + 4, [I,2]clad the linearization L(x) of f(x) at xa.14)

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Asked Dec 2, 2019
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Can you help me solve and understand number 11. (Shell method) thanks!

Sample nal
+2+
A2
Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves
about the given lines.
11) y = 4 - x2,
SLC
nsvia
y= 4,
x 2; revolve about the line y = 4
11)
Solve the initial value problem.
d3y
Icre
gmbib b
J5thobudgic 12)
12)
dx3
9: y" (0) 3, y'(0) 4, y(0) 5
f(b) f(a)
Find the value or values of c that satisfy the equation
f'(c) in the conclusion of the Mean Value Theore
b - a
he function and interval.
or
13)
13) f(x) = x2+ 3x + 4, [I,2]
cla
d the linearization L(x) of f(x) at x
a.
14)
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Sample nal +2+ A2 Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves about the given lines. 11) y = 4 - x2, SLC nsvia y= 4, x 2; revolve about the line y = 4 11) Solve the initial value problem. d3y Icre gmbib b J5thobudgic 12) 12) dx3 9: y" (0) 3, y'(0) 4, y(0) 5 f(b) f(a) Find the value or values of c that satisfy the equation f'(c) in the conclusion of the Mean Value Theore b - a he function and interval. or 13) 13) f(x) = x2+ 3x + 4, [I,2] cla d the linearization L(x) of f(x) at x a. 14)

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Expert Answer

Step 1

we graph the region first. 

We have to rotate the shaded region about y=4

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6 -5 3 2- 1- -5 -2 -4 -3 -1 5 -1 -2 --3 st LO O

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Step 2

r= radius=4-y

h=height = 2-x=2-sqrt(4-y)

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6 5 y= 4-x 3 4- 2- 4-y 1 -3 -5 -4 -1- -2 LC O

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Step 3

Put them in the sh...

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2nradiusxheight dy 2r (4-y)12-4-y ]dy -2[8-4/4-y-2y+y4-y ]dy

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