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Exam 17: Vector Calculus

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Exam 1: Functions226 Questionsadd course
Exam 2: Limits224 Questionsadd course
Exam 3: Derivatives367 Questionsadd course
Exam 4: Applications of the Derivative228 Questionsadd course
Exam 5: Integration166 Questionsadd course
Exam 6: Applications of Integration211 Questionsadd course
Exam 7: Logarithmic, Exponential, and Hyperbolic Functions85 Questionsadd course
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Exam 10: Sequences and Infinite Series173 Questionsadd course
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Exam 12: Parametric and Polar Curves169 Questionsadd course
Exam 13: Vectors and the Geometry of Space131 Questionsadd course
Exam 14: Vector-Valued Functions83 Questionsadd course
Exam 15: Functions of Several Variables229 Questionsadd course
Exam 16: Multiple Integration299 Questionsadd course
Exam 17: Vector Calculus173 Questionsadd course
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Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = 3yi + yj + zk; C: the counterclockwise path around the boundary of the ellipse Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = 3yi + yj + zk; C: the counterclockwise path around the boundary of the ellipse + = 1 + Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = 3yi + yj + zk; C: the counterclockwise path around the boundary of the ellipse + = 1 = 1

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Question 41

Find the flux of the curl of field F through the shell S. -F = -5 Find the flux of the curl of field F through the shell S. -F = -5 yi + 5x j + ln zk ; S: r(r, \theta ) = r cos \theta i + r sin \theta j + 2rk, 0 \le r \le 2 and 0 \le \theta \le 2 \pi yi + 5x Find the flux of the curl of field F through the shell S. -F = -5 yi + 5x j + ln zk ; S: r(r, \theta ) = r cos \theta i + r sin \theta j + 2rk, 0 \le r \le 2 and 0 \le \theta \le 2 \pi j + ln zk ; S: r(r, θ\theta ) = r cos θ\theta i + r sin θ\theta j + 2rk, 0 ≤\le r ≤\le 2 and 0 ≤\le θ\theta ≤\le 2 π\pi

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Question 42

Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder i + 9 Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder j + 4 Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder k ; C: the portion of the paraboloid Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder + Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder = z cut by the cylinder Use Stokes' Theorem to calculate the circulation of the field F around the curve C in the indicated direction. -F = -9 i + 9 j + 4 k ; C: the portion of the paraboloid + = z cut by the cylinder

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Question 43

Find the surface area of the surface S. -S is the surface Find the surface area of the surface S. -S is the surface + 9z = 0 that lies above the region bounded by the x-axis, and y = x. Find the surface area of the surface S. -S is the surface + 9z = 0 that lies above the region bounded by the x-axis, and y = x. + 9z = 0 that lies above the region bounded by the x-axis, Find the surface area of the surface S. -S is the surface + 9z = 0 that lies above the region bounded by the x-axis, and y = x. and y = x.

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Question 44

Evaluate the line integral along the curve C. -Evaluate the line integral along the curve C. -

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Question 45

Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = zk , S is the surface of the sphere Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = zk , S is the surface of the sphere + + = 25 in the first octant , direction away from the origin + Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = zk , S is the surface of the sphere + + = 25 in the first octant , direction away from the origin + Find the flux of the vector field F across the surface S in the indicated direction. -F(x, y, z) = zk , S is the surface of the sphere + + = 25 in the first octant , direction away from the origin = 25 in the first octant , direction away from the origin

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Question 46

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: the perimeter of the circle + = 16 + Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: the perimeter of the circle + = 16 , C: the perimeter of the circle Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: the perimeter of the circle + = 16 + Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: the perimeter of the circle + = 16 = 16

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Question 47

Calculate the circulation of the field F around the closed curve C. -Calculate the circulation of the field F around the closed curve C. - curve C is the counterclockwise path around curve C is the counterclockwise path around Calculate the circulation of the field F around the closed curve C. - curve C is the counterclockwise path around Calculate the circulation of the field F around the closed curve C. - curve C is the counterclockwise path around

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Question 48

Find the surface area of the surface S. -S is the portion of the surface Find the surface area of the surface S. -S is the portion of the surface that lies above the rectangle in the x-y plane. that lies above the rectangle Find the surface area of the surface S. -S is the portion of the surface that lies above the rectangle in the x-y plane. in the x-y plane.

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Question 49

Find the potential function f for the field F. -Find the potential function f for the field F. -

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Question 50

Find the flux of the vector field F across the surface S in the indicated direction. -Find the flux of the vector field F across the surface S in the indicated direction. - S is the upper hemisphere of x<sup>2</sup> + y<sup>2</sup> + z<sup>2</sup> = 25; direction is outward S is the upper hemisphere of x2 + y2 + z2 = 25; direction is outward

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Question 51

Calculate the area of the surface S. -S is the portion of the cone Calculate the area of the surface S. -S is the portion of the cone + = that lies between z = 3 and z = 5. + Calculate the area of the surface S. -S is the portion of the cone + = that lies between z = 3 and z = 5. = Calculate the area of the surface S. -S is the portion of the cone + = that lies between z = 3 and z = 5. that lies between z = 3 and z = 5.

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Question 52

Find the surface area of the surface S. -S is the area cut from the plane z = 10y by the cylinder Find the surface area of the surface S. -S is the area cut from the plane z = 10y by the cylinder + = 64. + Find the surface area of the surface S. -S is the area cut from the plane z = 10y by the cylinder + = 64. = 64.

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Question 53

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = y + x, C: Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = y + x, C: + = 4 in the first quadrant from ( 2, 0) to (0, 2) + Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = y + x, C: + = 4 in the first quadrant from ( 2, 0) to (0, 2) = 4 in the first quadrant from ( 2, 0) to (0, 2)

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Question 54

Find the flux of the curl of field F through the shell S. -F = Find the flux of the curl of field F through the shell S. -F = i + j + 3xyk; S is the portion of the paraboloid 2 - - = z that lies above the i + Find the flux of the curl of field F through the shell S. -F = i + j + 3xyk; S is the portion of the paraboloid 2 - - = z that lies above the j + 3xyk; S is the portion of the paraboloid 2 - Find the flux of the curl of field F through the shell S. -F = i + j + 3xyk; S is the portion of the paraboloid 2 - - = z that lies above the - Find the flux of the curl of field F through the shell S. -F = i + j + 3xyk; S is the portion of the paraboloid 2 - - = z that lies above the = z that lies above the Find the flux of the curl of field F through the shell S. -F = i + j + 3xyk; S is the portion of the paraboloid 2 - - = z that lies above the

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Question 55

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = x, C: y = Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = x, C: y = , 0 \le x \le , 0 ≤\le x ≤\le Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = x, C: y = , 0 \le x \le

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Question 56

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = , C: y = , 0 \le x \le 1 , C: y = Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = , C: y = , 0 \le x \le 1 , 0 ≤\le x ≤\le 1

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Question 57

Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: y = -2x - 4, 0 \le x \le 3 + Evaluate the line integral of f(x,y) along the curve C. -f(x, y) = + , C: y = -2x - 4, 0 \le x \le 3 , C: y = -2x - 4, 0 ≤\le x ≤\le 3

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Question 58

Sketch the vector field in the plane along with its horizontal and vertical components at a representative assortment of points on the circle x2 + y2 = 4. -F = -xi - yj

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Question 59

Find the flux of the curl of field F through the shell S. -F = ( 1 - y)i + ( 2 + x)j + Find the flux of the curl of field F through the shell S. -F = ( 1 - y)i + ( 2 + x)j + k; S is the upper hemisphere of + + = 16 k; S is the upper hemisphere of Find the flux of the curl of field F through the shell S. -F = ( 1 - y)i + ( 2 + x)j + k; S is the upper hemisphere of + + = 16 + Find the flux of the curl of field F through the shell S. -F = ( 1 - y)i + ( 2 + x)j + k; S is the upper hemisphere of + + = 16 + Find the flux of the curl of field F through the shell S. -F = ( 1 - y)i + ( 2 + x)j + k; S is the upper hemisphere of + + = 16 = 16

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