CALCULUS (CLOTH)
4th Edition
ISBN: 9781319050733
Author: Rogawski
Publisher: MAC HIGHER
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Chapter 18.1, Problem 33E
To determine
Find the value of .
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Sketch the vector field F.
F(x, y)
=
yi + xj
√x² + y²
2
Prove the following Product Rule:
curl(f F) = f curl(F) + ∇f × F
Show that V x (V.f) = 0 for any vector field f.
Chapter 18 Solutions
CALCULUS (CLOTH)
Ch. 18.1 - Prob. 1PQCh. 18.1 - Prob. 2PQCh. 18.1 - Prob. 3PQCh. 18.1 - Prob. 4PQCh. 18.1 - Prob. 5PQCh. 18.1 - Prob. 1ECh. 18.1 - Prob. 2ECh. 18.1 - Prob. 3ECh. 18.1 - Prob. 4ECh. 18.1 - Prob. 5E
Ch. 18.1 - Prob. 6ECh. 18.1 - Prob. 7ECh. 18.1 - Prob. 8ECh. 18.1 - Prob. 9ECh. 18.1 - Prob. 10ECh. 18.1 - Prob. 11ECh. 18.1 - Prob. 12ECh. 18.1 - Prob. 13ECh. 18.1 - Prob. 14ECh. 18.1 - Prob. 15ECh. 18.1 - Prob. 16ECh. 18.1 - Prob. 17ECh. 18.1 - Prob. 18ECh. 18.1 - Prob. 19ECh. 18.1 - Prob. 20ECh. 18.1 - Prob. 21ECh. 18.1 - Prob. 22ECh. 18.1 - Prob. 23ECh. 18.1 - Prob. 24ECh. 18.1 - Prob. 25ECh. 18.1 - Prob. 26ECh. 18.1 - Prob. 27ECh. 18.1 - Prob. 28ECh. 18.1 - Prob. 29ECh. 18.1 - Prob. 30ECh. 18.1 - Prob. 31ECh. 18.1 - Prob. 32ECh. 18.1 - Prob. 33ECh. 18.1 - Prob. 34ECh. 18.1 - Prob. 35ECh. 18.1 - Prob. 36ECh. 18.1 - Prob. 37ECh. 18.1 - Prob. 38ECh. 18.1 - Prob. 39ECh. 18.1 - Prob. 40ECh. 18.1 - Prob. 41ECh. 18.1 - Prob. 42ECh. 18.1 - Prob. 43ECh. 18.1 - Prob. 44ECh. 18.1 - Prob. 45ECh. 18.1 - Prob. 46ECh. 18.1 - Prob. 47ECh. 18.1 - Prob. 48ECh. 18.1 - Prob. 49ECh. 18.1 - Prob. 50ECh. 18.1 - Prob. 51ECh. 18.2 - Prob. 1PQCh. 18.2 - Prob. 2PQCh. 18.2 - Prob. 3PQCh. 18.2 - Prob. 4PQCh. 18.2 - Prob. 5PQCh. 18.2 - Prob. 1ECh. 18.2 - Prob. 2ECh. 18.2 - Prob. 3ECh. 18.2 - Prob. 4ECh. 18.2 - Prob. 5ECh. 18.2 - Prob. 6ECh. 18.2 - Prob. 7ECh. 18.2 - Prob. 8ECh. 18.2 - Prob. 9ECh. 18.2 - Prob. 10ECh. 18.2 - Prob. 11ECh. 18.2 - Prob. 12ECh. 18.2 - Prob. 13ECh. 18.2 - Prob. 14ECh. 18.2 - Prob. 15ECh. 18.2 - Prob. 16ECh. 18.2 - Prob. 17ECh. 18.2 - Prob. 18ECh. 18.2 - Prob. 19ECh. 18.2 - Prob. 20ECh. 18.2 - Prob. 21ECh. 18.2 - Prob. 22ECh. 18.2 - Prob. 23ECh. 18.2 - Prob. 24ECh. 18.2 - Prob. 25ECh. 18.2 - Prob. 26ECh. 18.2 - Prob. 27ECh. 18.2 - Prob. 28ECh. 18.2 - Prob. 29ECh. 18.2 - Prob. 30ECh. 18.2 - Prob. 31ECh. 18.2 - Prob. 32ECh. 18.2 - Prob. 33ECh. 18.2 - Prob. 34ECh. 18.2 - Prob. 35ECh. 18.2 - Prob. 36ECh. 18.2 - Prob. 37ECh. 18.2 - Prob. 38ECh. 18.3 - Prob. 1PQCh. 18.3 - Prob. 2PQCh. 18.3 - Prob. 3PQCh. 18.3 - Prob. 4PQCh. 18.3 - Prob. 5PQCh. 18.3 - Prob. 1ECh. 18.3 - Prob. 2ECh. 18.3 - Prob. 3ECh. 18.3 - Prob. 4ECh. 18.3 - Prob. 5ECh. 18.3 - Prob. 6ECh. 18.3 - Prob. 7ECh. 18.3 - Prob. 8ECh. 18.3 - Prob. 9ECh. 18.3 - Prob. 10ECh. 18.3 - Prob. 11ECh. 18.3 - Prob. 12ECh. 18.3 - Prob. 13ECh. 18.3 - Prob. 14ECh. 18.3 - Prob. 15ECh. 18.3 - Prob. 16ECh. 18.3 - Prob. 17ECh. 18.3 - Prob. 18ECh. 18.3 - Prob. 19ECh. 18.3 - Prob. 20ECh. 18.3 - Prob. 21ECh. 18.3 - Prob. 22ECh. 18.3 - Prob. 23ECh. 18.3 - Prob. 24ECh. 18.3 - Prob. 25ECh. 18.3 - Prob. 26ECh. 18.3 - Prob. 27ECh. 18.3 - Prob. 28ECh. 18.3 - Prob. 29ECh. 18.3 - Prob. 30ECh. 18.3 - Prob. 31ECh. 18.3 - Prob. 32ECh. 18.3 - Prob. 33ECh. 18.3 - Prob. 34ECh. 18.3 - Prob. 35ECh. 18.3 - Prob. 36ECh. 18.3 - Prob. 37ECh. 18.3 - Prob. 38ECh. 18.3 - Prob. 39ECh. 18.3 - Prob. 40ECh. 18.3 - Prob. 41ECh. 18.3 - Prob. 42ECh. 18.3 - Prob. 43ECh. 18.3 - Prob. 44ECh. 18 - Prob. 1CRECh. 18 - Prob. 2CRECh. 18 - Prob. 3CRECh. 18 - Prob. 4CRECh. 18 - Prob. 5CRECh. 18 - Prob. 6CRECh. 18 - Prob. 7CRECh. 18 - Prob. 8CRECh. 18 - Prob. 9CRECh. 18 - Prob. 10CRECh. 18 - Prob. 11CRECh. 18 - Prob. 12CRECh. 18 - Prob. 13CRECh. 18 - Prob. 14CRECh. 18 - Prob. 15CRECh. 18 - Prob. 16CRECh. 18 - Prob. 17CRECh. 18 - Prob. 18CRECh. 18 - Prob. 19CRECh. 18 - Prob. 20CRECh. 18 - Prob. 21CRECh. 18 - Prob. 22CRECh. 18 - Prob. 23CRECh. 18 - Prob. 24CRECh. 18 - Prob. 25CRECh. 18 - Prob. 26CRECh. 18 - Prob. 27CRECh. 18 - Prob. 28CRECh. 18 - Prob. 29CRECh. 18 - Prob. 30CRECh. 18 - Prob. 31CRECh. 18 - Prob. 32CRECh. 18 - Prob. 33CRECh. 18 - Prob. 34CRECh. 18 - Prob. 35CRECh. 18 - Prob. 36CRECh. 18 - Prob. 37CRECh. 18 - Prob. 38CRECh. 18 - Prob. 39CRECh. 18 - Prob. 40CRECh. 18 - Prob. 41CRE
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- B1. Advance mathsarrow_forwardThe nabla formulas corresponding to the derivative rule of income are gVf+fVg, (Vƒ). F + f(V.F), (Vf) x F + f(V x F). ▼(fg) V. (fF) ▼ x (fF) = = = Justify the middle one (e.g. in the case of n = 3). Hint: The coordinate functions of the vector field fF are fF₁ etcarrow_forwardAssume that u and u are continuously differentiable functions. Using Green's theorem, prove that Uz JE v|dA= [udv, Uy D where D is some domain enclosed by a simple closed curve C with positive orientation.arrow_forward
- 3) Compute the curl of F= (4 xy) i + (2x² + 2z²) j + (4 yz) k.arrow_forward1. Consider the vector-valued function F(t) = sin(2t) t (2, 1, -2), a) Find the domain of F. b) Show that F is continuous at t = 0. ; et, t 1-√1+t, t #0 t = 0. = (1/2/3/17, -2). 2. Consider the vector-valued function R(t) with R(1) = (1,2,−1) and R (t) = (1 a) Find '(1) if (t) = (-2, -3t, t²) × R'(t). b) Find the equation of the normal plane to the graph of Ả at t = 1. c) Find the arc length of the graph of R from the point at t = 1 to the point at t = 3. d) Find the curvature of the graph of R at t = 1.arrow_forward3. Let F = (2y² + z)i + 4.ryj + «k. (a) Show whether F is conservative. (b) Using the fundamental theorem of calculus for line integrals, prove that F. dr = -T along a curve C defined by a vector function r(t) = cos ti + sin tj + tk for 0arrow_forwardPlease help solve for the problem provided in the photo belowarrow_forwardsketch properly and provide full solutions! will give thumbs up!arrow_forward1. Consider the function f (x, y, z) = y- + y² +z? Determine the gradient vector field of f, F =Vf b. Determine the curl of F . How could you have predicted the result of part b? C.arrow_forwardarrow_back_iosarrow_forward_ios
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