Please describe the contour map and list important aspects of it, thanks!
Homework Answers
Given that
we have to find the vector field F(x,y) for which f(x,y) is a potential function.
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Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x, y) for which f(x, y...
(1)Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j (2)...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
Please answer without using previously posted answers. Thanks Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a g...
Please answer without using previously posted answers.
Thanks
Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a gradient field, and φ s called a potential function. Ideal Fluid Flow Let F represent the two-dimensional velocity field of an inviscid fluid that is incompressible, ie. . F-0 (or divergence-free). F can be represented by (1), where ф is called the velocity potential-show that o is harmonic....
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y)...
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y) = (3y, 22 – y). Suppose further that ^ C R2 is a curve in R2 consisting of the parabola y = 22 - 1 for 1 € (-1,0) and the straight line y = 1 – 1 for 1 € [0,1]. (i) Sketch the curvey in R2 [2] (ii) By considering the curve y piecewise, compute the vector field integral: [5] F(x). F(x)...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a conservative vector field. b.) Find the potential function of F. In other words, find a scalar function f(x, y, z) such that ✓ f = 7. Please show all steps. c.) Let C be any smooth curve starting at (1,1,1) and ending at (e, e, 1). Compute (Fdi. С
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a....
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...
1.) (12 pts.) Consider the vector field F(x, y, z) = (3x” 2 + 3 +...
1.) (12 pts.) Consider the vector field F(x, y, z) = (3x” 2 + 3 + yzbi – (22 - 1z)] + (23 – 2yz + 2 + xy). Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible,
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe" 1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector...
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
Problem 4. (15 points each) Let F(x, y, z) = (0, x, y) G(x, y, z)...
Problem 4. (15 points each) Let F(x, y, z) = (0, x, y) G(x, y, z) = (2x, z, y) + (x, y, z) = (3y, 2x, z). (a) For each field, either find a scalar potential function or prove that none exists. (b) For each field, either find a vector potential function or prove that none exists. (c) Let F(t) = (2, 2t, t2). For which of these vector fields is ñ a flow line? Justify your answer.
6. Let f be a scalar function and F be a vector field. Label each quantity...
6. Let f be a scalar function and F be a vector field. Label each quantity as a Scalar, Vector or Nonsense. Scalar Vector Nonsense Scalar Vector Nonsense curl F div F curl(curl F) div(curl F) Vf DO000 DDDDD D0000 V:(V F) VF div(div F) div(curl VF) curl (div F) 00000 DDDDD 00000
For any vector field F⃗ and any scalar function f we define a new field a) Assuming that the app...
For any vector field F⃗ and any scalar function f we define a new field
a) Assuming that the appropriate partial derivatives are
continuous, show the following formula:
b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field
Use the formula found in a) to answer
the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)?
f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
(1)Calculate the scalar curl of the vector field.
F(x, y) = sin(x)i + 6 cos(x)j
(2)
Let F(x, y, z) = (2exz, 3 sin(xy),
x7y2z6).
(a) Find the divergence of F.
(b)Find the curl of F.
-/3 points v MARSVECTORCALC6 4.4.017. My Notes Ask You Calculate the scalar curl of the vector field. F(x, y) = sin(x)i + 6 cos(x)j -/8 points v MARSVECTORCALC6 4.4.023. My Notes Ask You Let F(x, y, z) = (2x2, 3 sin(xy), x?y2z6). (a) Find...
Please answer without using previously posted answers.
Thanks
Let F(x, y) be a two-dimensional vector field. Spose further that there exists a scalar function, o, such that Then, F(x,y) is called a gradient field, and φ s called a potential function. Ideal Fluid Flow Let F represent the two-dimensional velocity field of an inviscid fluid that is incompressible, ie. . F-0 (or divergence-free). F can be represented by (1), where ф is called the velocity potential-show that o is harmonic....
(b) Let F: R2 + Rº be a vector field on R2 defined as F(x, y) = (3y, 22 – y). Suppose further that ^ C R2 is a curve in R2 consisting of the parabola y = 22 - 1 for 1 € (-1,0) and the straight line y = 1 – 1 for 1 € [0,1]. (i) Sketch the curvey in R2 [2] (ii) By considering the curve y piecewise, compute the vector field integral: [5] F(x). F(x)...
Let F = (2,1,1) be a vector field in Rº a.) Show that F is a conservative vector field. b.) Find the potential function of F. In other words, find a scalar function f(x, y, z) such that ✓ f = 7. Please show all steps. c.) Let C be any smooth curve starting at (1,1,1) and ending at (e, e, 1). Compute (Fdi. С
16. xyty Let f(x, y) = x3 + xy + y}, g(x, y) = x3 a. Show that there is a unique point P= (a,b) on 9(x,y) = 1 where fp = 1V9p for some scalar 1. b. Refer to Figure 13 to determine whether $ (P) is a local minimum or a local maximum of f subject to the constraint. c. Does Figure 13 suggest that f(P) is a global extremum subject to the constraint? 2 0 -3 -2...
1.) (12 pts.) Consider the vector field F(x, y, z) = (3x” 2 + 3 + yzbi – (22 - 1z)] + (23 – 2yz + 2 + xy). Find a scalar function f, which has a gradient vector equal to F, or determine that this is impossible,
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
1. Sketch the vector field F x, y+(y-x)j F(x, y x, y f 2. Find the gradient vector field of f(r, y)-xe"
Problem 4. (15 points each) Let F(x, y, z) = (0, x, y) G(x, y, z) = (2x, z, y) + (x, y, z) = (3y, 2x, z). (a) For each field, either find a scalar potential function or prove that none exists. (b) For each field, either find a vector potential function or prove that none exists. (c) Let F(t) = (2, 2t, t2). For which of these vector fields is ñ a flow line? Justify your answer.
6. Let f be a scalar function and F be a vector field. Label each quantity as a Scalar, Vector or Nonsense. Scalar Vector Nonsense Scalar Vector Nonsense curl F div F curl(curl F) div(curl F) Vf DO000 DDDDD D0000 V:(V F) VF div(div F) div(curl VF) curl (div F) 00000 DDDDD 00000
For any vector field F⃗ and any scalar function f we define a new field
a) Assuming that the appropriate partial derivatives are
continuous, show the following formula:
b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field
Use the formula found in a) to answer
the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)?
f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
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