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
To determine
To evaluate:The given line
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Students have asked these similar questions
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?
1. Please
Incorrect.
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.
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_forward1. Find the line integral in a vector field F. dr, where F = (y, x + 2y) and C is a curve consisting of 2 parts. First, the straight line from (-1,1) to (1,1), followed by the parabola y = x² from (1,1) to (2,4). You must show all your work.arrow_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 yı, , y5 and then fill in the blanks rounding your numbers to •.... three decimal places. X1 = i 1.1 ,Yi = i 2.51 X2 i 1.2 ,y2 3.273 X3 = i 1.3 ,Y3 = i 4.50283 X4 = i 1.4 , Y4 i 6.7162 X5 = i 1.5 , Y5 = i 11.4427 eTextbook and Media Hint I| ||arrow_forward
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