Calculus
7th Edition
ISBN: 9781524916817
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.3, Problem 4PS
To determine
To find: If the
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Chapter 13 Solutions
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
Ch. 13.1 - Prob. 11PSCh. 13.1 - Prob. 12PSCh. 13.1 - Prob. 13PSCh. 13.1 - Prob. 14PSCh. 13.1 - Prob. 15PSCh. 13.1 - Prob. 16PSCh. 13.1 - Prob. 17PSCh. 13.1 - Prob. 18PSCh. 13.1 - Prob. 19PSCh. 13.1 - Prob. 20PSCh. 13.1 - Prob. 21PSCh. 13.1 - Prob. 22PSCh. 13.1 - Prob. 23PSCh. 13.1 - Prob. 24PSCh. 13.1 - Prob. 25PSCh. 13.1 - Prob. 26PSCh. 13.1 - Prob. 27PSCh. 13.1 - Prob. 28PSCh. 13.1 - Prob. 29PSCh. 13.1 - Prob. 30PSCh. 13.1 - Prob. 31PSCh. 13.1 - Prob. 32PSCh. 13.1 - Prob. 33PSCh. 13.1 - Prob. 34PSCh. 13.1 - Prob. 35PSCh. 13.1 - Prob. 36PSCh. 13.1 - Prob. 37PSCh. 13.1 - Prob. 38PSCh. 13.1 - Prob. 39PSCh. 13.1 - Prob. 40PSCh. 13.1 - Prob. 41PSCh. 13.1 - Prob. 42PSCh. 13.1 - Prob. 43PSCh. 13.1 - Prob. 44PSCh. 13.1 - Prob. 45PSCh. 13.1 - Prob. 46PSCh. 13.1 - Prob. 47PSCh. 13.1 - Prob. 48PSCh. 13.1 - Prob. 49PSCh. 13.1 - Prob. 50PSCh. 13.1 - Prob. 51PSCh. 13.1 - Prob. 52PSCh. 13.1 - Prob. 53PSCh. 13.1 - Prob. 54PSCh. 13.1 - Prob. 55PSCh. 13.1 - Prob. 56PSCh. 13.1 - Prob. 57PSCh. 13.1 - Prob. 58PSCh. 13.1 - Prob. 59PSCh. 13.1 - Prob. 60PSCh. 13.2 - Prob. 1PSCh. 13.2 - Prob. 2PSCh. 13.2 - Prob. 3PSCh. 13.2 - Prob. 4PSCh. 13.2 - Prob. 5PSCh. 13.2 - Prob. 6PSCh. 13.2 - Prob. 7PSCh. 13.2 - Prob. 8PSCh. 13.2 - Prob. 9PSCh. 13.2 - Prob. 10PSCh. 13.2 - Prob. 11PSCh. 13.2 - Prob. 12PSCh. 13.2 - Prob. 13PSCh. 13.2 - Prob. 14PSCh. 13.2 - Prob. 15PSCh. 13.2 - Prob. 16PSCh. 13.2 - Prob. 17PSCh. 13.2 - Prob. 18PSCh. 13.2 - Prob. 19PSCh. 13.2 - Prob. 20PSCh. 13.2 - Prob. 21PSCh. 13.2 - Prob. 22PSCh. 13.2 - Prob. 23PSCh. 13.2 - Prob. 24PSCh. 13.2 - Prob. 25PSCh. 13.2 - Prob. 26PSCh. 13.2 - Prob. 27PSCh. 13.2 - Prob. 28PSCh. 13.2 - Prob. 29PSCh. 13.2 - Prob. 30PSCh. 13.2 - Prob. 31PSCh. 13.2 - Prob. 32PSCh. 13.2 - Prob. 33PSCh. 13.2 - Prob. 34PSCh. 13.2 - Prob. 35PSCh. 13.2 - Prob. 36PSCh. 13.2 - Prob. 37PSCh. 13.2 - Prob. 38PSCh. 13.2 - Prob. 39PSCh. 13.2 - Prob. 40PSCh. 13.2 - Prob. 41PSCh. 13.2 - Prob. 42PSCh. 13.2 - Prob. 43PSCh. 13.2 - Prob. 44PSCh. 13.2 - Prob. 45PSCh. 13.2 - Prob. 46PSCh. 13.2 - Prob. 47PSCh. 13.2 - 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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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- 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.arrow_forwardProblem B. For the vector field F(x, y) = 2y + 4x 7, i evaluate fF.dr over the line segment C from P(2,−4) to Q(1,2). JFarrow_forwardDraw a direction field (slope field) of y' = x. Use all 25 grid intersections. 2 1 2arrow_forward
- 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 sheetarrow_forwardDetermine 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_forwardSOLVE THE FOLLOWING COMPLETELY. 1. Given the vector field G = 2x²y ax-2(z-x) a, + 3xyz az, find: a. G at P(2,-3,4) b. A unit vector of G at P c. The scalar equation of the surface on which IG| = 100 d. The y coordinate of Q(-3, y, 5) if (G|=100 and y>0 e. Distance between P and Qarrow_forward
- 7. (Note: The three parts of this question are unrelated. Each one is about different vector fields.) (a) For each of the three vector fields below, first determine whether it is conservative and then find a potential function if it is: F₁ = (e + sin(y), xey – 2y) F₂ = (e³+ sin(x), xe² + 2y) 2 F3 = (xe" - sin(x), e² + 2y) (b) The vector field F = (7xy, e) is not conservative. Find the exact value of the integral of this vector field along the path C parametrized as r(t) = (t², t³) for −1 ≤t≤1. (c) The vector field F(x, y) = (-y sin(xy), -x sin(xy)) is the gradient vector field of the function f(x, y) = cos(xy). (That is, F = Vf.) Use this fact to evaluate the line integral where C is parametrized by r(t) = (1+½, t²-2t+π) for 0 ≤ t ≤ 2.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_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_forward
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