Filters
Question type
Study Flashcards

Let F be a vector field such that F = ∇φ - y i for some smooth scalar function φ. Evaluate Let F be a vector field such that F = ∇φ - y i for some smooth scalar function φ. Evaluate counterclockwise around the ellipse + = 1. counterclockwise around the ellipse Let F be a vector field such that F = ∇φ - y i for some smooth scalar function φ. Evaluate counterclockwise around the ellipse + = 1. + Let F be a vector field such that F = ∇φ - y i for some smooth scalar function φ. Evaluate counterclockwise around the ellipse + = 1. = 1.

Correct Answer

verifed

verified

Find the gradient vector field Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - kf(x,y) of f(x, y) = Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k .


A) - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k i - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k j - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k k
B) Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k i + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k j + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k k
C) Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k i + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k j + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k k
D) Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k i + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k j + Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k k
E) - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k i - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k j - Find the gradient vector field f(x,y) of f(x, y) = . A) - i - j - k B) i + j + k C) i + j + k D) i + j + k E) - i - j - k k

Correct Answer

verifed

verified

Use the fact that the field F = 2x Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 sin(z) i - Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 sin(z) j + ( Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 cos(z) + y) k is almost conservative (except for the last term) to help you evaluate Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 around the circle Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0 Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0


A) 2 π\pi
B) π\pi
C) Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0
D) Use the fact that the field F = 2x sin(z) i - sin(z) j + ( cos(z) + y) k is almost conservative (except for the last term) to help you evaluate around the circle A) 2 \pi B) \pi C) D) E) 0
E) 0

Correct Answer

verifed

verified

Find parametric equations of the streamline of the velocity field v(x, y, z) = y i - y j + y k that passes through the point (2, -3, -4) .


A) x = 2 + t, y = -3 - t, z = -4 + t
B) x = 2 + t, y = -3 + t, z = -4 + t
C) x = 2 + t, y = -3 - t, z = -4 - t
D) x = 2 + t, y = 3 - t, z = 4 + t
E) x = 2t, y = -3t, z = -4t

Correct Answer

verifed

verified

Evaluate the line integral Evaluate the line integral + x dy + z dz along the curve C from (1, 0, 1) to(-1, 2, 5) with parametrization with A) 9 B) 10 C) 11 D) 12 E) 8 + x dy + z dz along the curve C from (1, 0, 1) to(-1, 2, 5) with parametrization Evaluate the line integral + x dy + z dz along the curve C from (1, 0, 1) to(-1, 2, 5) with parametrization with A) 9 B) 10 C) 11 D) 12 E) 8 with Evaluate the line integral + x dy + z dz along the curve C from (1, 0, 1) to(-1, 2, 5) with parametrization with A) 9 B) 10 C) 11 D) 12 E) 8


A) 9
B) 10
C) 11
D) 12
E) 8

Correct Answer

verifed

verified

Let F be a smooth conservative force field defined in 2-space with a potential function Let F be a smooth conservative force field defined in 2-space with a potential function , and let C be the curve shown in the figure below. Find the work done by the force field F in moving a particle along the curve C from P to R given that φ(1,- 2) = -17, andφ(4, 1) = 3. , and let C be the curve shown in the figure below. Find the work done by the force field F in moving a particle along the curve C from P to R given that φ(1,- 2) = -17, andφ(4, 1) = 3. Let F be a smooth conservative force field defined in 2-space with a potential function , and let C be the curve shown in the figure below. Find the work done by the force field F in moving a particle along the curve C from P to R given that φ(1,- 2) = -17, andφ(4, 1) = 3.

Correct Answer

verifed

verified

The gradient of a scalar field The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r expressed in terms of polar coordinates [r, θ\theta ] in the plane is The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r (r, θ\theta ) = The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r + The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r . The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r Use the result above to find the necessary condition for the vector field F(r, θ\theta ) = P(r, θ\theta ) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r + Q(r, θ\theta ) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r to be conservative.


A) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r = The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r
B) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r = r The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r
C) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r = - The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r
D) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r - r The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r = Q
E) The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r - The gradient of a scalar field expressed in terms of polar coordinates [r, \theta ] in the plane is (r, \theta ) = + . Use the result above to find the necessary condition for the vector field F(r, \theta ) = P(r, \theta ) + Q(r, \theta ) to be conservative. A) = B) = r C) = - D) - r = Q E) - = r = r

Correct Answer

verifed

verified

Find the area element at a point r (θ, φ) on the parametric surface Find the area element at a point r (θ, φ) on the parametric surface , . , Find the area element at a point r (θ, φ) on the parametric surface , . .

Correct Answer

verifed

verified

(a) In terms of polar coordinates r and θ\theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and θ\theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j.


A) (a) radial lines θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = (b) circles r = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta =
B) (a) circles r = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = (b) radial lines θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta =
C) (a) circles r = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = sin( θ\theta ) (b) circles r = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = cos( θ\theta )
D) (a) lines r cos θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = (b) lines r sin θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta =
E) (a) lines r cos θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta = (b) radial lines θ\theta = (a) In terms of polar coordinates r and \theta , describe the field lines of the conservative plane vector field F(x,y) = x i + y j. (b) In terms of polar coordinates r and \theta , describe the equipotential curves of the conservative plane vector field F(x,y) = x i + y j. A) (a) radial lines \theta = (b) circles r = B) (a) circles r = (b) radial lines \theta = C) (a) circles r = sin( \theta ) (b) circles r = cos( \theta ) D) (a) lines r cos \theta = (b) lines r sin \theta = E) (a) lines r cos \theta = (b) radial lines \theta =

Correct Answer

verifed

verified

Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are and A) 2 square units B) 3 square units C) 4 square units D) 6 square units E) 1 square unit and Find the area of the region cut from the plane x + 2y + 2z = 5 by the cylinder whose walls are and A) 2 square units B) 3 square units C) 4 square units D) 6 square units E) 1 square unit


A) 2 square units
B) 3 square units
C) 4 square units
D) 6 square units
E) 1 square unit

Correct Answer

verifed

verified

How much work is required for the force field F = y i + 2x j to move an object along the upper part of the ellipse How much work is required for the force field F = y i + 2x j to move an object along the upper part of the ellipse from (3, 0) to (-3, 0) ? A) 2 \pi B) 9 \pi C) -9 \pi D) -2 \pi E) 0 from (3, 0) to (-3, 0) ?


A) 2 π\pi
B) 9 π\pi
C) -9 π\pi
D) -2 π\pi
E) 0

Correct Answer

verifed

verified

Compute the flux of F = z Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0 i - Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0 y j + (x - 2z) k upward across the square Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0 in the plane z = 1.


A) Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0
B) - Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0
C) - Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0
D) Compute the flux of F = z i - y j + (x - 2z) k upward across the square in the plane z = 1. A) B) - C) - D) E) 0
E) 0

Correct Answer

verifed

verified

Find the value of the positive constant real number a such that the area of the part of the plane Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E) inside the elliptic paraboloid z = 3x2 + ay2 is equal to Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E) square units.


A) Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E)
B) Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E)
C) Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E)
D) Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E)
E) Find the value of the positive constant real number a such that the area of the part of the plane inside the elliptic paraboloid z = 3x<sup>2</sup> + ay<sup>2</sup> is equal to square units. A) B) C) D) E)

Correct Answer

verifed

verified

If F = -y i + x j + z k, calculate If F = -y i + x j + z k, calculate where C is the straight line segment from(1, 0, 0) to (-1, 0, \pi ) . A) B) C) 1 D) E) \pi where C is the straight line segment from(1, 0, 0) to (-1, 0, π\pi ) .


A) If F = -y i + x j + z k, calculate where C is the straight line segment from(1, 0, 0) to (-1, 0, \pi ) . A) B) C) 1 D) E) \pi
B) If F = -y i + x j + z k, calculate where C is the straight line segment from(1, 0, 0) to (-1, 0, \pi ) . A) B) C) 1 D) E) \pi
C) 1
D) If F = -y i + x j + z k, calculate where C is the straight line segment from(1, 0, 0) to (-1, 0, \pi ) . A) B) C) 1 D) E) \pi
E) π\pi

Correct Answer

verifed

verified

Is F (x,y) = (3 Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative. y + 2x Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative. + 1) i + ( Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative. + 2 Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative. y + 1) j conservative? If so, find a potential for it.


A) Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative.
B) Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative.
C) Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative.
D) Is F (x,y) = (3 y + 2x + 1) i + ( + 2 y + 1) j conservative? If so, find a potential for it. A) B) C) D) E) No, it is not conservative.
E) No, it is not conservative.

Correct Answer

verifed

verified

Evaluate Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi where S is the part of the paraboloid 2x = 8 - Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi - Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi lying between the planes Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi


A) 2 π\pi Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi
B) 2 π\pi Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi
C) 2 π\pi Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi
D) π\pi Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi
E) π\pi Evaluate where S is the part of the paraboloid 2x = 8 - - lying between the planes A) 2 \pi B) 2 \pi C) 2 \pi D) \pi E) \pi

Correct Answer

verifed

verified

Let Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. = Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. , Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. = Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. and Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. = Let = , = and = be sets of points in 3-space. Determine whether the set is a connected or a simply connected set. A) S<sub>1</sub> is simply connected. B) S<sub>2</sub> is not connected. C) S<sub>1</sub> is connected but not simply connected. D) S<sub>3</sub> is simply connected. E) S<sub>3</sub> is connected but not simply connected. be sets of points in 3-space. Determine whether the set is a connected or a simply connected set.


A) S1 is simply connected.
B) S2 is not connected.
C) S1 is connected but not simply connected.
D) S3 is simply connected.
E) S3 is connected but not simply connected.

Correct Answer

verifed

verified

Compute the flux of F = Compute the flux of F = outward from the solid region \le z \le 1. A) -2 B) 2 C) 1 D) 0 E) -1 outward from the solid region Compute the flux of F = outward from the solid region \le z \le 1. A) -2 B) 2 C) 1 D) 0 E) -1 ≤\le z ≤\le 1.


A) -2
B) 2
C) 1
D) 0
E) -1

Correct Answer

verifed

verified

The function V(x,y) = 3 The function V(x,y) = 3 +3xy + 5 is a Liapunov function for the autonomous system associated with the vector field F = (y -7x) i + (3x - 5y) j in any domain D containing the fixed point at the origin. +3xy + 5 The function V(x,y) = 3 +3xy + 5 is a Liapunov function for the autonomous system associated with the vector field F = (y -7x) i + (3x - 5y) j in any domain D containing the fixed point at the origin. is a Liapunov function for the autonomous system associated with the vector field F = (y -7x) i + (3x - 5y) j in any domain D containing the fixed point at the origin.

Correct Answer

verifed

verified

Compute the flux of F = 2x i - Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0 j + (z - 2x + 2y) k upward through the part of the plane Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0 in the first octant of 3-space.


A) Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0
B) Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0
C) Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0
D) Compute the flux of F = 2x i - j + (z - 2x + 2y) k upward through the part of the plane in the first octant of 3-space. A) B) C) D) E) 0
E) 0

Correct Answer

verifed

verified

Showing 21 - 40 of 90

Related Exams

Exam 1

Preliminaries

127 Questions

Exam 2

Limits and Continuity

92 Questions

Exam 3

Differentiation

131 Questions

Exam 4

Transcendental Functions

129 Questions

Exam 5

More Applications of Differentiation

130 Questions

Exam 6

Integration

117 Questions

Exam 7

Techniques of Integration

118 Questions

Exam 8

Applications of Integration

139 Questions

Exam 9

Conics, Parametric Curves, and Polar Curves

114 Questions

Exam 10

Sequences, Series, and Power Series

125 Questions

Exam 11

Vectors and Coordinate Geometry in 3-Space

119 Questions

Exam 12

Vector Functions and Curves

87 Questions

Exam 13

Partial Differentiation

104 Questions

Exam 14

Applications of Partial Derivatives

67 Questions

Exam 15

Multiple Integration

105 Questions

Exam 17

Vector Calculus

92 Questions

Exam 18

Differential Forms and Exterior Calculus

76 Questions

Exam 19

Ordinary Differential Equations

135 Questions

Show Answer