Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and $\sigma$ is that portion of the sphere x2 + y2 + z2 = 4 for which z $\ge$ 0.

A) B) C) 0 D) E) A) B) C) 0 D) E)

Evaluate $\int$C 8xy dx - 8y2dy where C is the line segment from (0, 0) to (2, 1).

The answer of Evaluate $\int$C 8xy dx - 8y2dy where...

Use Stokes' Theorem to evaluate over the circle x2 + y2 = 1, z = 1.

Let @#LAT-DLM&be the portion of the plane z = 1 or

Evaluate where F(x, y, z) = -x i - 2x j + (z - 1)k and $\sigma$ is the surface enclosed by that portion of the paraboloid z = 4 - y2 which lies in the first octant and is bounded by the coordinate planes and the plane y = x. The surface is oriented by upward unit normals.

The answer of Evaluate where F(x, y, z)...

A) B) C) D) 0 E) A) B) C) D) 0 E)

Exam 15: Topics in Vector Calculus

Use Stokes' Theorem to evaluate $Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and \sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.$ where F(x, y, z) = $Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and \sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.$ (z - y)i + $Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and \sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.$ (z² + x)j + $Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and \sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.$ (x² - y²)k and $\sigma$ is that portion of the sphere x² + y² + z² = 4 for which z $\ge$ 0.

(Multiple Choice)

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Question 81

F (x, y, z) = 12xyz i + 12xyz j + 12xyz k. Find the outward flux of the vector field F across the cube with vertices (0, 0, 0), (0, 0, 2), (0, 2, 2), (2, 2, 2), (0, 2, 0), (2, 0, 0), (2, 2, 0), and (2, 0, 2).

(Short Answer)

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Question 82

Let . Find divF.

(Multiple Choice)

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Question 83

Evaluate $\int$ _C 8xy dx - 8y²dy where C is the line segment from (0, 0) to (2, 1).

(Short Answer)

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Question 84

Find div F and curl F of F(x, y, z) = 11x³y i + 11xy³ j + 2k.

(Essay)

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Question 85

Evaluate the line integral $Evaluate the line integral where C is the helix x = cos t, y = sin t, z = t, 0 \le t \le 2 \pi .$ where C is the helix x = cos t, y = sin t, z = t, 0 $\le$ t $\le$ 2 $\pi$ .

(Essay)

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Question 86

Use Stokes' Theorem to evaluate over the circle x² + y² = 1, z = 1.

(Essay)

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Question 87

Use Stokes' Theorem to evaluate $Use Stokes' Theorem to evaluate where F(x, y, z) = 11(z - y)i + 11(z2 + x)j + 11(x2 - y2)k and \sigma is that portion of the sphere x2 + y2 + z2 = 4 for which z \ge 0.$ where F(x, y, z) = 11(z - y)i + 11(z² + x)j + 11(x² - y²)k and $\sigma$ is that portion of the sphere x² + y² + z² = 4 for which z $\ge$ 0.

(Multiple Choice)

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Question 88

Use Green's Theorem to evaluate , where C is the square bounded by x = y = 0, and x = y = 1.

(Multiple Choice)

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Question 89

Evaluate $Evaluate where F(x, y, z) = -x i - 2x j + (z - 1)k and \sigma is the surface enclosed by that portion of the paraboloid z = 4 - y2 which lies in the first octant and is bounded by the coordinate planes and the plane y = x. The surface is oriented by upward unit normals.$ where F(x, y, z) = -x i - 2x j + (z - 1)k and $\sigma$ is the surface enclosed by that portion of the paraboloid z = 4 - y² which lies in the first octant and is bounded by the coordinate planes and the plane y = x. The surface is oriented by upward unit normals.

(Essay)

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Question 90

Evaluate $Evaluate where F(x, y, z) = 9y i - 9x j - 36z2 k and \sigma is that portion of the cone which lies above the square in the xy-plane with vertices (0, 0), (1, 0), (1, 1), and (0, 1), and oriented by downward unit normals.$ where F(x, y, z) = 9y i - 9x j - 36z² k and $\sigma$ is that portion of the cone $Evaluate where F(x, y, z) = 9y i - 9x j - 36z2 k and \sigma is that portion of the cone which lies above the square in the xy-plane with vertices (0, 0), (1, 0), (1, 1), and (0, 1), and oriented by downward unit normals.$ which lies above the square in the xy-plane with vertices (0, 0), (1, 0), (1, 1), and (0, 1), and oriented by downward unit normals.

(Multiple Choice)

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Question 91

F(x, y, z) = 7x² i + [$A]j + 3xyz k. Find div F.

(Short Answer)

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Question 92

Let . Find curlF.

(Multiple Choice)

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Question 93

Use the divergence theorem to evaluate $Use the divergence theorem to evaluate where , n is the outer unit normal to \sigma , and \sigma is the surface of the sphere by x2 + y2 + z2 = 49.$ where $Use the divergence theorem to evaluate where , n is the outer unit normal to \sigma , and \sigma is the surface of the sphere by x2 + y2 + z2 = 49.$ , n is the outer unit normal to $\sigma$ , and $\sigma$ is the surface of the sphere by x² + y² + z² = 49.

(Multiple Choice)

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Question 94

Let $Let and let \sigma be a closed, orientable surface that surrounds the origin. Then the flux \phi =$ and let $\sigma$ be a closed, orientable surface that surrounds the origin. Then the flux $\phi$ =

(Multiple Choice)

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Question 95

Evaluate the surface integral $Evaluate the surface integral , where \sigma is the portion of the cone r(u, v) = u cos v i + u sin v j + u k for which 1 \le u \le 2, .$ , where $\sigma$ is the portion of the cone r(u, v) = u cos v i + u sin v j + u k for which 1 $\le$ u $\le$ 2, $Evaluate the surface integral , where \sigma is the portion of the cone r(u, v) = u cos v i + u sin v j + u k for which 1 \le u \le 2, .$ .

(Essay)

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Question 96

Is F(x, y) = 5x i + 5y j is a conservative vector field?

(Short Answer)

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Question 97

Let . Find divF.

(Multiple Choice)

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Question 98

Use Stokes' Theorem to evaluate $\int$ _C -4yz dx + 4xz dy + 4xy dz where C is the circle x² + y² = 2, z = 1.

(Multiple Choice)

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Question 99

Find div F and curl F of .

(Essay)

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Question 100

Showing 81 - 100 of 149

F (x, y, z) = 12xyz i + 12xyz j + 12xyz k. Find the outward flux of the vector field F across the cube with vertices (0, 0, 0), (0, 0, 2), (0, 2, 2), (2, 2, 2), (0, 2, 0), (2, 0, 0), (2, 2, 0), and (2, 0, 2).

Let . Find divF.

Evaluate $\int$ _C 8xy dx - 8y²dy where C is the line segment from (0, 0) to (2, 1).

Find div F and curl F of F(x, y, z) = 11x³y i + 11xy³ j + 2k.

Evaluate the line integral $Evaluate the line integral where C is the helix x = cos t, y = sin t, z = t, 0 \le t \le 2 \pi .$ where C is the helix x = cos t, y = sin t, z = t, 0 $\le$ t $\le$ 2 $\pi$ .

Use Stokes' Theorem to evaluate over the circle x² + y² = 1, z = 1.

Use Green's Theorem to evaluate , where C is the square bounded by x = y = 0, and x = y = 1.

F(x, y, z) = 7x² i + [$A]j + 3xyz k. Find div F.

Let . Find curlF.

Let $Let and let \sigma be a closed, orientable surface that surrounds the origin. Then the flux \phi =$ and let $\sigma$ be a closed, orientable surface that surrounds the origin. Then the flux $\phi$ =

Is F(x, y) = 5x i + 5y j is a conservative vector field?

Let . Find divF.

Use Stokes' Theorem to evaluate $\int$ _C -4yz dx + 4xz dy + 4xy dz where C is the circle x² + y² = 2, z = 1.

Find div F and curl F of .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

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Parametric and Polar Curves; Conic Sections

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Exam 15: Topics in Vector Calculus

Use Stokes' Theorem to evaluate where F(x, y, z) = (z - y)i + (z2 + x)j + (x2 - y2)k and σ\sigmaσ is that portion of the sphere x2 + y2 + z2 = 4 for which z ≥\ge≥ 0.

F (x, y, z) = 12xyz i + 12xyz j + 12xyz k. Find the outward flux of the vector field F across the cube with vertices (0, 0, 0), (0, 0, 2), (0, 2, 2), (2, 2, 2), (0, 2, 0), (2, 0, 0), (2, 2, 0), and (2, 0, 2).

Let . Find divF.

Evaluate ∫\int∫ C 8xy dx - 8y2dy where C is the line segment from (0, 0) to (2, 1).

Find div F and curl F of F(x, y, z) = 11x3y i + 11xy3 j + 2k.

Evaluate the line integral where C is the helix x = cos t, y = sin t, z = t, 0 ≤\le≤ t ≤\le≤ 2 π\piπ .

Use Stokes' Theorem to evaluate over the circle x2 + y2 = 1, z = 1.

Use Stokes' Theorem to evaluate where F(x, y, z) = 11(z - y)i + 11(z2 + x)j + 11(x2 - y2)k and σ\sigmaσ is that portion of the sphere x2 + y2 + z2 = 4 for which z ≥\ge≥ 0.

Use Green's Theorem to evaluate , where C is the square bounded by x = y = 0, and x = y = 1.

Evaluate where F(x, y, z) = -x i - 2x j + (z - 1)k and σ\sigmaσ is the surface enclosed by that portion of the paraboloid z = 4 - y2 which lies in the first octant and is bounded by the coordinate planes and the plane y = x. The surface is oriented by upward unit normals.

Evaluate where F(x, y, z) = 9y i - 9x j - 36z2 k and σ\sigmaσ is that portion of the cone which lies above the square in the xy-plane with vertices (0, 0), (1, 0), (1, 1), and (0, 1), and oriented by downward unit normals.

F(x, y, z) = 7x2 i + [$A]j + 3xyz k. Find div F.

Let . Find curlF.

Use the divergence theorem to evaluate where , n is the outer unit normal to σ\sigmaσ , and σ\sigmaσ is the surface of the sphere by x2 + y2 + z2 = 49.

Let and let σ\sigmaσ be a closed, orientable surface that surrounds the origin. Then the flux ϕ\phiϕ =

Evaluate the surface integral , where σ\sigmaσ is the portion of the cone r(u, v) = u cos v i + u sin v j + u k for which 1 ≤\le≤ u ≤\le≤ 2, .

Is F(x, y) = 5x i + 5y j is a conservative vector field?

Let . Find divF.

Use Stokes' Theorem to evaluate ∫\int∫ C -4yz dx + 4xz dy + 4xy dz where C is the circle x2 + y2 = 2, z = 1.

Find div F and curl F of .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Three-Dimensional Space; Vectors

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Filters

Evaluate $\int$ _C 8xy dx - 8y²dy where C is the line segment from (0, 0) to (2, 1).

Find div F and curl F of F(x, y, z) = 11x³y i + 11xy³ j + 2k.

Evaluate the line integral $Evaluate the line integral where C is the helix x = cos t, y = sin t, z = t, 0 \le t \le 2 \pi .$ where C is the helix x = cos t, y = sin t, z = t, 0 $\le$ t $\le$ 2 $\pi$ .

Use Stokes' Theorem to evaluate over the circle x² + y² = 1, z = 1.

F(x, y, z) = 7x² i + [$A]j + 3xyz k. Find div F.

Let $Let and let \sigma be a closed, orientable surface that surrounds the origin. Then the flux \phi =$ and let $\sigma$ be a closed, orientable surface that surrounds the origin. Then the flux $\phi$ =

Use Stokes' Theorem to evaluate $\int$ _C -4yz dx + 4xz dy + 4xy dz where C is the circle x² + y² = 2, z = 1.