Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
6th Edition
ISBN: 9781524908102
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 38SP
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To evaluate:The given line
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Suppose that over a certain region of space the electrical potential V is given by the following
equation.
V(x,v,z)= 5x2 – 2xy + xyz
In which direction does V change most rapidly at P(5, 2, 4)?
(24,10,10>
b. (54,4, – 8)
а.
c. (54,10,10>
d. (24,2,8)
e. (54,10, – 10>
Suppose that over a certain region of space the electrical potential V is given by the following equation.
V(x, y, z) = 4x² – 3xy + xyz
-
(a) Find the rate of change of the potential at P(2, 4, 5) in the direction of the vector v = i + j - k.
9
(b) In which direction does V change most rapidly at P?
(c) What is the maximum rate of change at P?
Suppose that over a certain region of space the electrical potential V is given by the following equation.
V(x, y, z) = 2x² - 5xy + xyz
(a) Find the rate of change of the potential at P(6, 6, 7) in the direction of the vector v = i + j - k.
(36,12,36)
(b) In which direction does V change most rapidly at P?
(c) What is the maximum rate of change at P?
Chapter 13 Solutions
Calculus: Special Edition: Chapters 1-5 (w/ WebAssign)
Ch. 13.1 - Prob. 1PSCh. 13.1 - Prob. 2PSCh. 13.1 - Prob. 3PSCh. 13.1 - Prob. 4PSCh. 13.1 - Prob. 5PSCh. 13.1 - Prob. 6PSCh. 13.1 - Prob. 7PSCh. 13.1 - Prob. 8PSCh. 13.1 - Prob. 9PSCh. 13.1 - Prob. 10PS
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- Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 3xy + xyz (a) Find the rate of change of the potential at P(5, 2, 5) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? 73°F Mostly cloudy (c) What is the maximum rate of change at P? Need Help? Read It Show My Work (Optional)? Watch It Qarrow_forwardIncorrect. Use a computer or calculator with Euler's method to approximate the flow line through (1, 2) for the vector field v = y² i +1.1x² j using 5 steps with At = 0.1. Find the exact values of x1, ... , x5 and y1, ... , y5 and then fill in the blanks rounding your numbers to three decimal places. X1 = !Yı = i X2 i 1.2 , y2 3.273 X3 = i 1.3 Y3 = i 4.50283 X4 i 1.4 6.7162 X5 = i 1.5 Y5 = i 11.4427 eTextbook and Media Assistance Used Hint Assistance Used The vector field is given by v = y i + 1.1x² j , that is, the flow line (x (t), y (t)) satisfies x' (t) = y² y' (t) = 1.1x².arrow_forwardSuppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) 3x2 — 3xy + xyz (a) Find the rate of change of the potential at P(2, 6, 5) in the direction of the vector v = i + j − k. = (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?arrow_forward
- Determine the signs of the line integrals for the pictured vector fields and curves. C₂ (a) (b) C₁ (c) √67 F.dr dr ---Select--- 6.7. 7. dr---Select--- V C₂ √₂7. d² dr (d) Sc.7. dr -- Select.. ---Select--- ✓ Oarrow_forwardSuppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 5x² - 5xy + xyz (a) Find the rate of change of the potential at P(4, 4, 7) in the direction of the vector v = i + j − k. (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P?arrow_forward
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