Study Guide for Stewart's Multivariable Calculus, 8th
8th Edition
ISBN: 9781305271845
Author: Stewart, James
Publisher: Brooks Cole
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Chapter 12.3, Problem 1PT
For a = 2i + 3j − 4k and b = −i + 2j − k, a · b =
- a) 0
- b) 8
- c) 10
- d) 12
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Use the shell method to find the volume of the solid generated by revolving the region bounded by x = 3√y, x = -y,
and y = 2 about the x-axis.
The answer is A
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Chapter 12 Solutions
Study Guide for Stewart's Multivariable Calculus, 8th
Ch. 12.1 - Prob. 1PTCh. 12.1 - Prob. 2PTCh. 12.1 - Prob. 3PTCh. 12.1 - Prob. 4PTCh. 12.1 - Prob. 5PTCh. 12.2 - Prob. 1PTCh. 12.2 - Prob. 2PTCh. 12.2 - Prob. 3PTCh. 12.2 - Prob. 4PTCh. 12.2 - Prob. 5PT
Ch. 12.2 - Prob. 6PTCh. 12.3 - For a = 2i + 3j 4k and b = i + 2j k, a b = a) 0...Ch. 12.3 - Prob. 2PTCh. 12.3 - Prob. 3PTCh. 12.3 - Prob. 4PTCh. 12.3 - Prob. 5PTCh. 12.3 - Prob. 6PTCh. 12.4 - Prob. 1PTCh. 12.4 - Prob. 2PTCh. 12.4 - Prob. 3PTCh. 12.4 - Prob. 4PTCh. 12.4 - Prob. 5PTCh. 12.4 - Prob. 6PTCh. 12.5 - The equation of the line through (4, 10, 8) and...Ch. 12.5 - True or False: These lines are skew:...Ch. 12.5 - The equation of the plane through 7, 2, 3 with...Ch. 12.5 - The equation of the plane formed by the two lines...Ch. 12.5 - The distance from (1, 2, 1) to the plane 6x + 5y +...Ch. 12.5 - A normal vector to the plane 2x + 3y + 6z =20 is:...Ch. 12.6 - Prob. 1PTCh. 12.6 - Prob. 2PTCh. 12.6 - Prob. 3PTCh. 12.6 - The graph at the right has equation: a)...Ch. 12.6 - Prob. 5PTCh. 12.6 - Prob. 6PT
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- The answer is B, Could you please show the steps to obtain the answerarrow_forward2. Suppose that U(x, y, z) = x² + y²+ z² represents the temperature of a 3-dimensional solid object at any point (x, y, z). Then F(x, y, z) = -KVU (x, y, z) represents the heat flow at (x, y, z) where K > 0 is called the conductivity constant and the negative sign indicates that the heat moves from higher temperature region into lower temperature region. Answer the following questions. (A) [90%] Compute the inward heat flux (i.e., the inward flux of F) across the surface z = 1 - x² - y². (B) [10%] Use the differential operator(s) to determine if the heat flow is rotational or irrotational.arrow_forwardCould you show why the answer is B Using polar coordinates and the area formulaarrow_forward
- 1. The parametric equations x = u, y = u cos v, z = usin v, with Ou≤ 2, 0 ≤ v ≤ 2π represent the cone that is obtained by revolving (about x-axis) the line y = x (for 0 ≤ x ≤2) in the xy-plane. Answer the following questions. (A) [50%] Sketch the cone and compute its surface area, which is given by dS = [ | Ər Or ди მა × du dv with S being the cone surface and D being the projection of S on the uv-plane. (B) [50%] Suppose that the density of the thin cone is σ(x, y, z) = 0.25x gr/cm². Compute the total mass of the cone.arrow_forwardThe value of sin (2V · F) at x = 3, y = 3, z = −4, where F -0.592 -0.724 0.661 -0.113 -0.822 -0.313 0.171 0.427 = (-2x² + -4,2yz − x − 3, −5xz - 2yz), isarrow_forwardThe correct answer is C Could you show me whyarrow_forward
- The graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = -4. Select all that apply: ☐ f(x) is not continuous at x = -4 because it is not defined at x = −4. ☐ f(x) is not continuous at x = -4 because lim f(x) does not exist. x-4 f(x) is not continuous at x = -4 because lim f(x) = f(−4). ☐ f(x) is continuous at x = -4. x-4 ين من طلب نہ 1 2 3 4 5 6 7arrow_forwardThe graph of f(x) is given below. Select each true statement about the continuity of f(x) at x = -1. -7-6-5 N HT Select all that apply: ☐ f(x) is not continuous at x = -1 because it is not defined at x = -1. ☐ f(x) is not continuous at -1 because lim f(x) does not exist. x-1 ☐ f(x) is not continuous at x = -1 because lim f(x) = f(−1). ☐ f(x) is continuous at x = -1. x-1 5 6 7arrow_forwardUse the shell method to find the volume of the solid generated by revolving the region bounded by the curves and lines about the y-axis. y=x², y=7-6x, x = 0, for x≥0arrow_forward
- The graph of f(x) is given below. Select all of the true statements about the continuity of f(x) at x = −3. -7-6- -5- +1 23456 1 2 3 4 5 67 Select the correct answer below: ○ f(x) is not continuous at x = f(x) is not continuous at x = f(x) is not continuous at x = f(x) is continuous at x = -3 -3 because f(-3) is not defined. -3 because lim f(x) does not exist. 2-3 -3 because lim f(x) = f(−3). 2-3arrow_forwardCould you explain how this was solved, I don’t understand the explanation before the use of the shift property As well as the simplification afterwardsarrow_forwardQuestion The function f(x) is shown in the graph below. Which of the following statements are true? Select all that apply. f(x) 12 10 -16 -14 -12 -10 -8 + -4 " 10 12 14 16 a Select all that apply: ☐ Condition 1 is satisfied. ☐ Condition 2 is satisfied. ☐ Condition 3 is satisfied. ☐ f(x) is continuous.arrow_forward
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