Calculus
6th Edition
ISBN: 9781465208880
Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE
Publisher: Kendall Hunt Publishing
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Chapter 13.1, Problem 11PS
To determine
To find: The divergence and the curl for 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
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- 1. Consider two vector fields: F1(x, y) = -yi+ xj and F2(7) = F. (a) Evaluate F and F, at the given points. (x, y) (1,0) (0, 1) (-1,0) (0, –1) F(r, y) F(1, y) (т, у) (1,1) (-1,1) (-1,–1) (1, –1) F(1, y) F(x, y) On the grids shown below, sketch above vectors of vector fields F (b) and F. F;(x, y) = -yi + xj F2(F) = F.arrow_forward1. A(np)2. Unit vector in the direction of vector field A at point P.arrow_forward6. Vector fields V and W are defined by V %3D (2х — Зу + z, -3х — у + 4z, 4y + z) W%3D (2x — 4y — 5z, -4х + 2у, -5х + 62) Determine which vector field is conservative and denote it by F.arrow_forward
- 8. A particle follows a straight-line path from (1,2) to (5,7) within the vector field F(x, y) = (xy, y²). Find the work. (That is, find f F dr where C is the path of the particle.)arrow_forward5. Let F(x, y) = square region with vertices (0,0), (1,0), (1, 1), and (0, 1) oriented counterclockwise. Find f F · dī exactly. Simplify your answer. (tan-y, -) be a vector field and let C be the boundary of the You must show all your work in a step by step manner, clearly, by the same way you learned in this class. No calculator output or decimal approximations are accepted.arrow_forwardIf a vector field F = (x+2y+ az)î + (bx-3y-z)7+ (4x+ cy + 2z) k is irrotational then the value of a, b,c are А. -4, -2,—1 В. -4, -2,1 С. 4,-2, —1 D. 4, 2,-1arrow_forward
- Match each of the functions (a)-(c) with the corresponding gradient vector field from those in (I)-(VI). Enter your answer as upper case roman numerals: I, II, III, etc. (a) f(x, y) = x cos(y) (b) f(x, y) = (x - 2)²(y-2)/5 (c) f(x, y) = sin(x) · cos(y) (click on an image to enlarge it) IV II V II VIarrow_forward5. Show that F= (y cos(x),sin(x)+ y) is a conservative vector field and use this to calculate the work done by F in moving a particle from (7/4,1) to (27/3,3).arrow_forwardthis is my last attemptarrow_forward
- 1. (Section 17.1) Match the vector fields with their sketches below by placing the letter of the function in the corresponding blank: (I) F(x, y) = (II) F(x, y) = (III) F(x, y) = (IV) F(x, y) = Vector Field: (B) Vector Field: (A) (C) Vector Field (D) 0 Vector Field:arrow_forward10. Given F(x, y) = (x, y), find the flux of the vector field across the piece of the circle x² + y² = 9 that begins at (3, 0) and ends at (-3, 0).arrow_forward2. Find a formula for curl(curl(u)) in terms of (x1, x2, x3) and (e,, e2, e3) if u = ujei + Uze2 + Uze3 and each of the u; is a double differentiable on R3.arrow_forward
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