Question

1)| The region bounded by f(x)=−1x^2+5x+14 x=0, and y=0 is
rotated about the *y*-axis. Find the volume of the solid of
revolution.

Find the exact value; write answer without decimals.

2) Now compute s4, the partial sum consisting of the first 4 terms of ∞∑k=1/7√k5:

s4=

3) Test the series below for convergence using the Ratio
Test.

∞∑n=1 n^2/0.9^n

The limit of the ratio test simplifies to limn→∞|f(n)| where

f(n)=

The limit is:

Answer #1

40) The region bounded by f(x)=−2x^2+12x+32, x=0 and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answers without decimals.

1) The region bounded by f(x)=−3x^2+18x+21, x=0, and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answer without decimals.
2) Suppose you lift a laptop that weighs 3.2 pounds off the
floor onto a shelf that is 4 feet high. How much work have you
done?
foot-pounds
3) The force on a particle is described by 9x^3−1 pounds at a point
xx feet along the x-axis. Find the work...

1) A volume is described as follows:
1. the base is the region bounded by y=2−2/25x^2 and y=0
2. every cross-section parallel to the x-axis is a
triangle whose height and base are equal.
Find the volume of this object.
volume =
2) The region bounded by f(x)=−4x^2+24x+108, x=0, and y=0 is
rotated about the y-axis. Find the volume of the solid of
revolution.
Find the exact value; write answer without decimals.

1. The region bounded by y=x8 and y=sin(πx/2) is
rotated about the line x=−7.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.
2.The region bounded by y=9/(1+x2), y=0, x=0 and x=8
is rotated about the line x=8.
Using cylindrical shells, set up an integral for the volume of the
resulting solid.

The region bounded by ?=2+sin?, ?=0, ?=0 and 2? is revolved
about the ?y-axis. Find the volume that results.
Hint:
∫?sin???=sin?−?cos?+?
Volume of the solid of revolution:

The region bounded by y=2^x and y=4x-4 is rotated
about the line y=3. Find the volume of the resulting solid.

1. Find the area bounded by f(x)=3x^2-4 and y=0 for 0 < X
< 1.
A. 1 B. 2 C. 6 D. 3
2. The revenue (thousands of dollars) from producing x units of
an item is modeled by R(x)= 5x-0.0005x^2. Find the marginal revenue
at x=1000.
A. $104 B. $4 C. $4.50 D. $10,300
3. Find y' for y=y(x) defined implicitly by 3xy-x^2-4=0
4. Find: lim x->-1 6x+5/5x-6
A. -11 B. 1/11 C. -1/11
D....

Find the volume of the solid of revolution formed by rotating
about the x-axis the region bounded by the curves
f(x)=4x^2
y=0
x=1
x=2
___
What is the volume in cubic units? (Exact answer using
π as needed)

The region bounded by the given curves is rotated about the
specified axis. Find the volume V of the resulting solid
by any method.
x = (y −
9)2, x =
16; about y = 5
V =

Consider the region bounded by f(x) = x^3 + x + 3 and y = 0 over
[−1, 2].
a) Find the partition of the given interval into n subintervals
of equal length. (Write ∆x, x0, x1, x2, · · · , xk, · · · ,
xn.)
b) Find f(xk), and setup the Riemann sum ∑k=1 f(xk)∆x.
c) Simplify the Riemann sum using the Power Sum Formulas.
d) Find the area of the region by taking limit as n...

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