The integration by parts formula is / udv : MU 0 du. Integration by parts is useful for
the antiderivative of a product of functions that cant otherwise be handled with usubstitution.
The two functions involved in the product could be:
1. Logarithmic:
Two identical boxes are moved in equal distances in the horizontal
direction. Box A experiences a constant net force F applied at an angle to
the horizontal and box B experiences.The correct answer is: The amount
of work done on each box cannot be determi
Three pool balls of equal mass are resting on a horizontal frictionless
surface. The cue ball (Ball 1) of mass 700 g is rolled.The answer is B: v
= 3.00 m / s F = 42.0 N
A rolling pin rolls down a 2-m incline, 30 degree ,
25k*m^2,5kg,15cm.The correct answ
If y = 0 is chosen to be at the ground level, which of the following is the
gravitational potential energy of a 500 lb weight that was lifted 3 ft from
ground level?.The correct answer is:1.50x10 ftlb
A 0.500 kg steel ball is dropped from a height of 4.00
A ride at an amusement park begins by spinning patrons about a circle of
radius R with constant speed v. At some point during the ride the speed
doubles a?.The correct answer is: a
The raising and lowering motion of this robotic arm is controlled by a rod
A steel playground slide is 5.25 m long and is raised 2.75 m on one end. A
45.0 kg child slides down from the top starting at rest. The final speed
bottom is 6.81 m/s.The correct answer is: 31.7 N
A person is lifting an object of mass M using an ideal rop
A bar weighting 100 N and 2 m in length, is held up by two strings that are
made out of different materials. The string on the left will break if the
tension goesThe correct answer is: 0.71 m
The hanging object shown in the diagram has a mass of 10 kg and
The radius of the Moon is known to be 1.7 10 m. Astronauts who walked
on the Moon measured the time it takes an object to fall 1 m on the Moon
to be about.The correct answer is: 7.1 10 kg
Using the conversion factor between kilograms and pounds, 1 kg = 2.
A uniform disk of mass M and radius R is rotating on an axle with constant
angular velocity W. MR^2The correct answer is C:1/6MR^2W^2
What would happen to the precession of a gyroscope if it were spinning in
the opposite direction?.The correct answer is:
The distance along both the axes, as shown in the drawing below, are in
meters. Which of the following is the resultant gravitational force vector
acting on the 100 kg mass at the origin of the diagram? The correct answer
is:B
Given a vector A as shown in
A small airplane and a hot air balloon are moving horizontally towards each
other. Relative to the ground, the plane travels at a speed of 135 m / s and
the balloon travels at a speed of 7 m/s.The correct answer is: 170 m /
s
The main pipe coming into a
From the following choices select the one that is not required for making
quantitative statements about the worldThe correct answer is: a
regional unit system
Sue throws Sam the keys to the car. The keys leave Sues hand at a height
of 1.2 m from the groun
When turning around a circle, a car is subject to a continuous force, but its
speed does not necessarily change.The correct answer is: The speed is
not changing, but the direction is.
How fast, in m / s, is a bug moving if it is sitting 10 cm from the cen
Which of following is the resultant gravitational force acting on the 100 kg
mass in the diagram?.The correct answer is C: 1.56x10^-6N
How many centimeters are in 2.3 meters?.The correct answer is: 230 cm
Which of this following is the gravitational force
Suppose the two rods A and B are moving at two speeds (1/4)c and (3/4)c,
respectively, relative to an observer O at rest. .The correct answer
is:LA>LB
If a radius of a pipe carrying water is doubled, the volume flow rate of the
water.The correct answer is
Paul has a mass M and a volume VpThe correct answer is:PwVpgmg
An observer O notes a particle moving to the right with velocity v. Another
observer O is moving with speed v relative to O along the direction of the
motion of the particle.The correct answer
You are in a mall and are hurrying to get to the candy store before it closes.
You walk on an escalator to speed up your progress.The correct
answer is: 1.6 s
Which of the following is correct concerning the centripetal acceleration of
an object in unifor
A ceiling fan has four blades. The distance between the center of the fan
and the tip of the blade is 0.75 m. The fan is spinning at 300 rev / min
The correct answer is: 75.5g
When a small car pulls a trailer for a move, which of the following explains
wh
The MichelsonMorley experiment is important in the context of Einsteins
special theory of relativity primarily because.The correct answer is: it
indicated that there is no absolute frame of reference from which to
measure the speed of light.
Two traffic c
In a game of marbles, a 60 g marble is rolling at 8.00 cm / s when it collides
with a stationary marble. the 60 g marble takes off at a 27. The correct
answer is: 0.0800 kg
A 309 g glass rolls down an incline and onto a horizontal platform where it
hits a
What is the acceleration of a skydiver at terminal velocity whose mass is 80
kg and cross-sectional area is 14 m2.The correct answer is: 0 m / sec2
Consider a spring that is stretched from its equilibrium position x , where x
= 0, to a position x, where x
1. A are is red upward from the ground at 100 ft/s. Findvthe
the are after 5 8. Bonus: Find its velocity at that moment. 3. Use the trapezoid rule to approximate f: mkzdx, With 4 subintervals of
>
equal length.
t".
. . 4. Find the volume of the solid gen
' r n 7 a . I
. ( E ., . K J 5. KE
.A 71 / ', 2V .- 5 11. s
l. Integrate: /3$2.1n(5:c)d$ _ JiJ ' K . Q X 7i J2 x
5/? .
7
m t 3 M: Li ZEXZ
h f
Sjg'i(gwii WCEEBQX3EElH 7
Jr 63 s m
f ' \1 Eff 'f/w . 3?
J 1W 4r: L5. M03941
x ~ m
mgyy :5
11)
Work the following integrals on the assigned ticms like w, 7%: Sim, cow, ext etc, it will
days to practice for the gateway If you be helpful to memorize the following so that
get stuck, a brief hints le isde on Manhat- you dont have to recreate. them on t
Solutions to Section 10.3 handout
s
, 1
1. (a) Use the'series for .
) 1 m
'1 _ 1 _
l+x2_l(a:2)_
=1x2+x4a:6+-
(b) Use the series for cos x.
22 24 26
3 2_ 3 (a?) (90) (93)
cc cos(a:):c (l 2! + 4! 6! +
m 3 $7 $11 $15
"727 E_F+
(c) Use the series fo
Review Exercises and Problems for Chapter 10 (p. 543)
2. Heres the chart:
Therefore
P2(x) =1n2+-;(x 2) + ;l/4(w 2)2
_ 1 1 ' 2
1n2+2(:c 2) 8(222).
3. Heres the chart:
Therefore
P2<x>=-%+%<m 2) "1W 92
7T 2
=%+-J-a<w+z>+<w+2)
So the Taylor series i
Review Exercises from Chapter 9 (pp. 497-499)
NOTE: Some of these are just answers /hints instead of full solutions. You should work out all the
details! l
2.
'14.
28.
29.
30.
31.
32.
33.
34.
36.
37.
The rst term is (0.5)3 and the ratio is 0.5. It equals