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1.) (8 pts.) Consider the vector field F(t, y, z) = (3cʻz + 3 + yzbi...
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,
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz,...
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x...
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where...
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i +...
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a...
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i...
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?)...
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...
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...
Please describe the contour map and list important aspects of
it, thanks!
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) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch.
Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >...
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
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,
96. Consider a vector field F(x, y, z) =< x + x cos(yz), 2y - eyz, z- xy > and scalar function f(x, y, z) = xy3e2z. Find the following, or explain why it is impossible: a) gradF (also denoted VF) b) divF (also denoted .F) c) curl(f) (also denoted xf) d) curl(gradf) (also denoted V x (0f) e) div(curlF) (also denoted 7. (V x F))
D Question 11 12 pts to Consider the vector field F (x, y, z) =< 2x – yz, 2y – az,2z – xy>. a) (3) Is this vector field conservative? Justify your answer. b) (9) Find the amount of work done by this vector field in moving a particle along the curve (t) =< 3cost, cos’t, cos” (2t) > from t = 0 tot = 1
10.) (19 pts.) Verify Stoke's Theorem for the Vector Field F(x, y, z) = (-y)ī+(x)]+(z)k, where Surface S is that portion of the paraboloid z = 6 - 22 - y2, which lies above the plane z = 2.
8.) (12 pts.) Find the Flux of the Vector Field F(x, y, z) = (z)i + (x)} + (y)k through Surface S, which is that portion of the plane 2++2 = 3 is the 1st octant, and r is the unit normal vector pointing away from the origin.
Prove that the following vector field F = 4xi +z j +(y – 2z)k is a gradient field, which means F is a conservative field and the work of F is path independent? Show all your work. a) Find f(x,y,z) whose gradient is equal to F. Is the line integral ſi. · di path independent? b) Find the line integral, or work of the force F along any trajectory from point Q:(-10, 2,5) to point P: (7,-3, 12).
8.) (16 pts.) Verify Stoke's Theorem for the Vector Field F (, y, z) = (-y)i + (-2)5+(z)k, where Surface S is that portion of the paraboloid z= 6 – 12 – yº, which lies above the plane z = 2.
DETAILS 3. [2/4 Points) Consider the given vector field. F(x, y, z) = (e", ely, exy?) (a) Find the curl of the vector field. - yzelyz lazenz curl Fe (b) Find the divergence of the vector field. div F = ertxely tuxely F. dr This question has several pa You will use Stokes' Theorem to rewrite the integral and C is the boundary of the plane 5x+3y +z = 1 in the fir F-(1,2-2, 2-3v7) oriented counterclockwise as viewed from...
Please describe the contour map and list important aspects of
it, thanks!
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) is a potential function, b) c) sketch a contour map of f (x, y) and, on the same figure, sketch F(x,y) (on R2). Comment on any important aspects of your sketch.
Let f(x,y) -2(xy 1) be a scalar function in R2. a) Find the vector field F(x,...
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-< ye", e + z,y >
Decide whether or not the vector field is a gradient field (i.e. is conservative). If it is conservative, find a potential function. (ii) F(x,y)-6ญ่-12xVJ (iv) F(x, y, z)-
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