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Let Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . where Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . and Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . . Let Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . be a sector of angle Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . in the sphere of radius Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . , centered at the origin and oriented outward. Find Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find . . Let where and . Let be a sector of angle in the sphere of radius , centered at the origin and oriented outward. Find .

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Compute the work performed in moving a particle along the path Compute the work performed in moving a particle along the path by the force by the force Compute the work performed in moving a particle along the path by the force

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Evaluate Evaluate for the path C shown in the following figure. The path consists of the line segment from (1, 0, 0) to (0, 1, 0), followed by the circular arc in the yz-plane with radius 1 joining (0, 1, 0) to (0, 0, 1). for the path C shown in the following figure. The path consists of the line segment from (1, 0, 0) to (0, 1, 0), followed by the circular arc in the yz-plane with radius 1 joining (0, 1, 0) to (0, 0, 1). Evaluate for the path C shown in the following figure. The path consists of the line segment from (1, 0, 0) to (0, 1, 0), followed by the circular arc in the yz-plane with radius 1 joining (0, 1, 0) to (0, 0, 1).

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Evaluate Evaluate where C is the line segment joining the points and where C is the line segment joining the points Evaluate where C is the line segment joining the points and and Evaluate where C is the line segment joining the points and

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Let Let A) Compute B) Evaluate where C is the parametric curve from to A) Compute Let A) Compute B) Evaluate where C is the parametric curve from to B) Evaluate Let A) Compute B) Evaluate where C is the parametric curve from to where C is the parametric curve Let A) Compute B) Evaluate where C is the parametric curve from to from Let A) Compute B) Evaluate where C is the parametric curve from to to Let A) Compute B) Evaluate where C is the parametric curve from to

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Find the surface area of the portion of the cone Find the surface area of the portion of the cone within the cylinder within the cylinder Find the surface area of the portion of the cone within the cylinder

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Compute the work performed in moving a particle along the path Compute the work performed in moving a particle along the path by the force by the force Compute the work performed in moving a particle along the path by the force

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Calculate the work performed by the force field Calculate the work performed by the force field on a particle that moves in the counterclockwise direction around the quarter circle . Assume that is in Newtons and the unit of distance is the meter. on a particle that moves in the counterclockwise direction around the quarter circle Calculate the work performed by the force field on a particle that moves in the counterclockwise direction around the quarter circle . Assume that is in Newtons and the unit of distance is the meter. . Assume that Calculate the work performed by the force field on a particle that moves in the counterclockwise direction around the quarter circle . Assume that is in Newtons and the unit of distance is the meter. is in Newtons and the unit of distance is the meter.

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Let Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to . A) Determine whether Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to has a potential function, and if so, find a potential function for Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to . B) Compute Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to where Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to , Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to is the curve Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to , Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to from Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to to Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to and Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to is the straight line from Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to to Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to Let . A) Determine whether has a potential function, and if so, find a potential function for . B) Compute where , is the curve , from to and is the straight line from to

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Compute the surface integral Compute the surface integral where and is the surface of the sphere centered at the origin with radius 4. where Compute the surface integral where and is the surface of the sphere centered at the origin with radius 4. and Compute the surface integral where and is the surface of the sphere centered at the origin with radius 4. is the surface of the sphere centered at the origin with radius 4.

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Compute Compute where S is the surface oriented upward and . where S is the surface Compute where S is the surface oriented upward and . oriented upward and Compute where S is the surface oriented upward and . .

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The area of the surface The area of the surface is which of the following? A) B) C) D) E) None of the answers is correct. is which of the following?


A) The area of the surface is which of the following? A) B) C) D) E) None of the answers is correct.
B) The area of the surface is which of the following? A) B) C) D) E) None of the answers is correct.
C) The area of the surface is which of the following? A) B) C) D) E) None of the answers is correct.
D) The area of the surface is which of the following? A) B) C) D) E) None of the answers is correct.
E) None of the answers is correct.

F) A) and E)
G) A) and C)

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Let Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . . A) Determine whether Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . is conservative, and if so, find a potential function for Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . B) Compute the integral Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . where C is the path Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . from Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . to Let . A) Determine whether is conservative, and if so, find a potential function for B) Compute the integral where C is the path from to . .

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Evaluate Evaluate where S is the surface cut from the paraboloid by the planes , and . where S is the surface cut from the paraboloid Evaluate where S is the surface cut from the paraboloid by the planes , and . by the planes Evaluate where S is the surface cut from the paraboloid by the planes , and . , Evaluate where S is the surface cut from the paraboloid by the planes , and . and Evaluate where S is the surface cut from the paraboloid by the planes , and . . Evaluate where S is the surface cut from the paraboloid by the planes , and .

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The integral The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) where The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) and S is the closed surface determined by the planes The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) , and The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E) and oriented outward is equal to which of the following?


A) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E)
B) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E)
C) 0
D) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E)
E) The integral where and S is the closed surface determined by the planes , and and oriented outward is equal to which of the following? A) B) C) 0 D) E)

F) A) and B)
G) B) and D)

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Define Define where Compute the vector assigned to the point by the vector field where Define where Compute the vector assigned to the point by the vector field Compute the vector assigned to the point Define where Compute the vector assigned to the point by the vector field by the vector field Define where Compute the vector assigned to the point by the vector field

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Compute the work performed in moving a particle along the path Compute the work performed in moving a particle along the path by the force by the force Compute the work performed in moving a particle along the path by the force

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Compute the line integral Compute the line integral where C is the line segment from to and . where C is the line segment from Compute the line integral where C is the line segment from to and . to Compute the line integral where C is the line segment from to and . and Compute the line integral where C is the line segment from to and . .

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Find the flux of Find the flux of across the surface , oriented outward. across the surface Find the flux of across the surface , oriented outward. , oriented outward.

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Define Define At what points is normal to the vector At what points is Define At what points is normal to the vector normal to the vector Define At what points is normal to the vector

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