Student's Solution and Survival Manual for Calculus
7th Edition
ISBN: 9781524934040
Author: STRAUSS MONTY J, TODA MAGDALENA DANIELE, SMITH KARL J
Publisher: Kendall Hunt Publishing
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Chapter 13, Problem 1SP
To determine
To check:whether the given
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Determine if each of the following vector fields is the gradient of a function f(x, y). If so, find all of the
functions with this gradient.
(a) (3x² + e¹0) i + (10x e¹0 - 9 siny) j
(b) (10x el0y 9 sin y) i + (3x² + e¹0y) j
a) I have placed my work and my answer on my answer sheet
7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where
F2 vanishes. Plot a few flow lines.
8. Repeat the previous problem for F = yî + (x − y)î.
Chapter 13 Solutions
Student's Solution and Survival Manual for Calculus
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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Prob. 3PSCh. 13.6 - Prob. 4PSCh. 13.6 - Prob. 5PSCh. 13.6 - Prob. 6PSCh. 13.6 - Prob. 7PSCh. 13.6 - Prob. 8PSCh. 13.6 - Prob. 9PSCh. 13.6 - Prob. 10PSCh. 13.6 - Prob. 11PSCh. 13.6 - Prob. 12PSCh. 13.6 - Prob. 13PSCh. 13.6 - Prob. 14PSCh. 13.6 - Prob. 15PSCh. 13.6 - Prob. 16PSCh. 13.6 - Prob. 17PSCh. 13.6 - Prob. 18PSCh. 13.6 - Prob. 19PSCh. 13.6 - Prob. 20PSCh. 13.6 - Prob. 21PSCh. 13.6 - Prob. 22PSCh. 13.6 - Prob. 23PSCh. 13.6 - Prob. 24PSCh. 13.6 - Prob. 25PSCh. 13.6 - Prob. 26PSCh. 13.6 - Prob. 27PSCh. 13.6 - Prob. 28PSCh. 13.6 - Prob. 29PSCh. 13.6 - Prob. 30PSCh. 13.6 - Prob. 31PSCh. 13.6 - Prob. 32PSCh. 13.6 - Prob. 33PSCh. 13.6 - Prob. 34PSCh. 13.6 - Prob. 35PSCh. 13.6 - Prob. 36PSCh. 13.6 - Prob. 37PSCh. 13.6 - Prob. 38PSCh. 13.6 - Prob. 39PSCh. 13.6 - Prob. 40PSCh. 13.6 - Prob. 41PSCh. 13.6 - Prob. 42PSCh. 13.6 - Prob. 43PSCh. 13.6 - Prob. 44PSCh. 13.6 - Prob. 45PSCh. 13.6 - Prob. 46PSCh. 13.6 - Prob. 47PSCh. 13.6 - Prob. 48PSCh. 13.6 - Prob. 49PSCh. 13.6 - Prob. 50PSCh. 13.6 - 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Prob. 40PSCh. 13.7 - Prob. 41PSCh. 13.7 - Prob. 42PSCh. 13.7 - Prob. 43PSCh. 13.7 - Prob. 44PSCh. 13.7 - Prob. 45PSCh. 13.7 - Prob. 46PSCh. 13.7 - Prob. 47PSCh. 13.7 - Prob. 48PSCh. 13.7 - Prob. 49PSCh. 13.7 - Prob. 50PSCh. 13.7 - Prob. 51PSCh. 13.7 - Prob. 52PSCh. 13.7 - Prob. 53PSCh. 13.7 - Prob. 54PSCh. 13.7 - Prob. 55PSCh. 13.7 - Prob. 56PSCh. 13.7 - Prob. 57PSCh. 13.7 - Prob. 58PSCh. 13.7 - Prob. 59PSCh. 13.7 - Prob. 60PSCh. 13 - Prob. 1PECh. 13 - Prob. 2PECh. 13 - Prob. 3PECh. 13 - Prob. 4PECh. 13 - Prob. 5PECh. 13 - Prob. 6PECh. 13 - Prob. 7PECh. 13 - Prob. 8PECh. 13 - Prob. 9PECh. 13 - Prob. 10PECh. 13 - Prob. 11PECh. 13 - Prob. 12PECh. 13 - Prob. 13PECh. 13 - Prob. 14PECh. 13 - Prob. 15PECh. 13 - Prob. 16PECh. 13 - Prob. 17PECh. 13 - Prob. 18PECh. 13 - Prob. 19PECh. 13 - Prob. 20PECh. 13 - Prob. 21PECh. 13 - Prob. 22PECh. 13 - Prob. 23PECh. 13 - Prob. 24PECh. 13 - Prob. 25PECh. 13 - Prob. 26PECh. 13 - Prob. 27PECh. 13 - Prob. 28PECh. 13 - Prob. 29PECh. 13 - Prob. 30PECh. 13 - 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- 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.arrow_forward5. Given the vector field F (2у — 4г — 2) і + (2 — 2у) 5 (a) Show that the vector field is a gradient vector field. F (b) Find the potential function for the given vector field. (c) Evaluate the integral , Fdrwhere L is any curve connecting the points A = (-1, 2) and В %3 (2, 1) (d) What is the value of fc Fdr where C is a closed curve.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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