Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 13.1, Problem 2PT
The curve given by r(t) = 2i + tj + 2tk is a:
- a) line
- b) plane
- c) spiral
- d) circle
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Let R be the region bounded by the following curves. Let S be the solid generated when R is revolved about the given axis. If possible, find the volume of S by both the disk/washer and shell methods. Check that your results agree.
y=(x-2)³-3, x=0, y = 122; revolved about the y-axis
Set up the integral(s) that gives the volume of the solid as a single integral if possible using the disk/washer method. Use increasing limits of integration. Select the correct choice below and fill in any answer boxes within your choice.
OA. Ody+
dy (Type exact answers.)
OB. dy (Type exact answers.)
(dy
Set up the integral(s) that gives the volume of the solid as a single integral if possible using the shell method. Use increasing limits of integration. Select the correct choice below and fill in any answer boxes within your choice.
OA. dx (Type exact answers.)
OB. dx + [
dx (Type exact answers.)
The volume of the solid is
(Type an exact answer.)
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Find the arc length of the following curve on the given interval.
1
2
In x-
y =
4
2
on [3,12]
1
The arc length of y = In x-
on [3,12] is
2
(Type an exact answer.)
Evaluate the following integral.
In
| Im² (x²) ox
DXC
In 2 (x²)
X
dx = (Type an integer or a simplified fraction.)
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Chapter 13 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 13.1 - For r(t)=sinticost4j,r(3)= a) 32i+22j b) 22i+32j...Ch. 13.1 - The curve given by r(t) = 2i + tj + 2tk is a: a)...Ch. 13.1 - Prob. 3PTCh. 13.1 - Prob. 4PTCh. 13.1 - Prob. 5PTCh. 13.2 - For r(t)=t3i+sintj(t2+2t)k,r(0)= a) j 2k b) 3i ...Ch. 13.2 - True or False: [r(t)s(t)]=r(t)s(t)+s(t)r(t).Ch. 13.2 - Prob. 3PTCh. 13.2 - Prob. 4PTCh. 13.3 - Prob. 1PT
Ch. 13.3 - Prob. 2PTCh. 13.3 - Prob. 3PTCh. 13.3 - Prob. 4PTCh. 13.3 - Prob. 5PTCh. 13.3 - True or False: If f is twice differentiable and x0...Ch. 13.3 - Prob. 7PTCh. 13.4 - Prob. 1PTCh. 13.4 - Find the position function for which (at t = 0)...Ch. 13.4 - The force needed for a 10-kg object to attain...Ch. 13.4 - Prob. 4PT
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- Determine the area of the shaded region bounded by y=-x2 +8x and y = x²-6x. The area of the region is (Type an exact answer.arrow_forwardEvaluate the following integral using integration by parts. x sin 16x dx √x sir x sin 16x dx =arrow_forwardA spring on a horizontal surface can be stretched and held 0.8 m from its equilibrium position with a force of 88 N. a. How much work is done in stretching the spring 2.5 m from its equilibrium position? b. How much work is done in compressing the spring 4.5 m from its equilibrium position? a. Set up the integral that gives the work done in stretching the spring 2.5 m from its equilibrium position. Use increasing limits of integration dx Od (Type exact answers.) The amount of work done is (Simplify your answer) b. Set up the integral that gives the work done in compressing the spring 4.5 m from its equilibrium position. Use decreasing limits of integration. dx (Type exact answers.) The amount of work done is (Simplify your answer) งarrow_forward
- E| Consider an object moving along a line with the given velocity v. Assume t is time measured in seconds and velocities have units of a. Determine when the motion is in the positive direction and when it is in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. v(t)=2t2-16t+14, [0,8] a. When is the motion in the positive direction? Select the correct choice and, if necessary, fill in the answer box to complete your choice OA. The motion is in the positive direction for t-values in the interval(s) (Use a comma to separate answers as needed. Type your answers in interval notation.) OB. The motion is never in the positive direction. When is the motion in the negative direction? Select the correct choice and, if necessary, fill in the answer box to complete your choice. OA. The motion is in the negative direction for t-values in the interval(s) (Use a comma to separate answers as needed. Type your answers in…arrow_forwardFind the volume of the solid generated when the region bounded by y =6x and y = 18√x is revolved about the x-axis. The volume of the solid is (Type an exact answer.) cubic units.arrow_forwardA drag racer accelerates at a(t)=66 ft/s2. Assume that v(0) = 0 and s(0) = 0. a. Determine the position function for t≥0. b. How far does the racer travel in the first 4 s? c. At this rate, how long will it take the racer to travel mi? 3 d. How long will it take the racer to travel 300 ft? e. How far has the racer traveled when it reaches a speed of 180 ft/s? a. The position function for t 20 is s(t) = b. In the first 4 s, the racer travels ft. (Simplify your answer. Type an integer or decimal rounded to three decimal places as needed.). c. At this rate, it will take the racer s to travel 13 mi. (Do not round until the final answer. Then round to three decimal places as needed.) d. It will take the racer s to travel 300 ft. (Do not round until the final answer. Then round to three decimal places as needed.) ft e. When the racer reaches a speed of 180 ft/s, it has traveled (Do not round until the final answer. Then round to three decimal places as needed.)arrow_forward
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