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Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = yi + xj (a) Show that F is conservative. ƏN ?х = ƏM ду (b) Verify that the value of To F. dr is the same for each parametric representation of C. (i) C₁: r₁(t) = (5 + t)i + (6 - t)j, 0 st≤ 1 [For . dr = (ii) C₂: r₂(w) = (5+ In(w))i + (6 - In(w))j, 1 ≤ w se SC₂F. F. dr =

Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = yi + xj (a) Show that F is conservative. ƏN ?х = ƏM ду (b) Verify that the value of To F. dr is the same for each parametric representation of C. (i) C₁: r₁(t) = (5 + t)i + (6 - t)j, 0 st≤ 1 [For . dr = (ii) C₂: r₂(w) = (5+ In(w))i + (6 - In(w))j, 1 ≤ w se SC₂F. F. dr =

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.2: Inner Product Spaces
Problem 101E: Consider the vectors u=(6,2,4) and v=(1,2,0) from Example 10. Without using Theorem 5.9, show that...
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Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = yi + xj (a) Show that F is conservative. ƏN ax = ƏM ду (b) Verify that the value of To F. dr is the same for each parametric representation of C. (i) C₁:₁ (t) = (5 + t)i + (6 - t)j, 0 st≤ 1 [For . dr = (ii) C₂: r₂(w) = (5+ In(w))i + (6 - In(w))j, 1 ≤ w ≤e SC₂F. F. dr =
Transcribed Image Text:Consider the following vector field F(x, y) = Mi + Nj. F(x, y) = yi + xj (a) Show that F is conservative. ƏN ax = ƏM ду (b) Verify that the value of To F. dr is the same for each parametric representation of C. (i) C₁:₁ (t) = (5 + t)i + (6 - t)j, 0 st≤ 1 [For . dr = (ii) C₂: r₂(w) = (5+ In(w))i + (6 - In(w))j, 1 ≤ w ≤e SC₂F. F. dr =
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