Question

1-6 Determine whether F is a conservative vector field. If so, find a potential function for it. 1. F(x, y) = xi + yj 2. F(x, y) = 3y^2i + 6xyj 3. F(x, y) = x^2yi + 5xy^2j 4. F(x, y) = e^x cos yi - e^x sin yj 5. F(x, y) = (cos y + y cos x)i + (sin x - x sin y)j

          1-6 Determine whether F is a conservative vector field. If so, find a potential function for it.
1. F(x, y) = xi + yj
2. F(x, y) = 3y^2i + 6xyj
3. F(x, y) = x^2yi + 5xy^2j
4. F(x, y) = e^x cos yi - e^x sin yj
5. F(x, y) = (cos y + y cos x)i + (sin x - x sin y)j

1-6 Determine whether F is a conservative vector field. If so, find a potential function for it.
1. F(x, y) = xi + yj
2. F(x, y) = 3y^2i + 6xyj
3. F(x, y) = x^2yi + 5xy^2j
4. F(x, y) = e^x cos yi - e^x sin yj
5. F(x, y) = (cos y + y cos x)i + (sin x - x sin y)j

Added by Andrew G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2023

Step 1

F(x,y) = xi + yj The partial derivatives are: ∂F1/∂x = 1, ∂F1/∂y = 0, ∂F2/∂x = 0, ∂F2/∂y = 1 Since ∂F1/∂y = ∂F2/∂x, F is conservative. A potential function f(x,y) can be found by integrating: ∫F1 dx = ∫x dx = (1/2)x^2 + g(y) ∫F2 dy = ∫y dy = (1/2)y^2 + Show more…

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Determine whether F is a conservative vector field. If so, find a potential function for it: 1. F(x,y) = xi + yj 2. F(x,y) = 3y^2i + 6xyj 3. F(x,y) = x^2yi + 5xy^2j 4. F(x,y) = e^x cos yi - e^x sin yj 5. F(x,y) = (cos y + y cos x)i + (sin x - x sin y)j