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Determine the largest set on which the function is continuous. Determine the largest set on which the function is continuous. A) B) C) D) E)


A) Determine the largest set on which the function is continuous. A) B) C) D) E)
B) Determine the largest set on which the function is continuous. A) B) C) D) E)
C) Determine the largest set on which the function is continuous. A) B) C) D) E)
D) Determine the largest set on which the function is continuous. A) B) C) D) E)
E) Determine the largest set on which the function is continuous. A) B) C) D) E)

F) B) and C)
G) B) and E)

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Determine where the function Determine where the function is continuous. A) B) C) D) is continuous.


A) Determine where the function is continuous. A) B) C) D)
B) Determine where the function is continuous. A) B) C) D)
C) Determine where the function is continuous. A) B) C) D)
D) Determine where the function is continuous. A) B) C) D)

E) A) and D)
F) C) and D)

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Evaluate the limit. Evaluate the limit. A) B) 0 C) D) E)


A) Evaluate the limit. A) B) 0 C) D) E)
B) 0
C) Evaluate the limit. A) B) 0 C) D) E)
D) Evaluate the limit. A) B) 0 C) D) E)
E) Evaluate the limit. A) B) 0 C) D) E)

F) B) and E)
G) All of the above

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Find the indicated partial derivative. Find the indicated partial derivative. A) B) C) D) E)


A) Find the indicated partial derivative. A) B) C) D) E)
B) Find the indicated partial derivative. A) B) C) D) E)
C) Find the indicated partial derivative. A) B) C) D) E)
D) Find the indicated partial derivative. A) B) C) D) E)
E) Find the indicated partial derivative. A) B) C) D) E)

F) A) and C)
G) A) and B)

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Use the Chain Rule to find Use the Chain Rule to find A) B) C) D) Use the Chain Rule to find A) B) C) D)


A) Use the Chain Rule to find A) B) C) D)
B) Use the Chain Rule to find A) B) C) D)
C) Use the Chain Rule to find A) B) C) D)
D) Use the Chain Rule to find A) B) C) D)

E) All of the above
F) B) and C)

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Use Lagrange multipliers to find the maximum and minimum values of the function Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints and . subject to the constraints Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints and . and Use Lagrange multipliers to find the maximum and minimum values of the function subject to the constraints and . .

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Use Lagrange multipliers to find the maximum value of the function subject to the given constraints. Use Lagrange multipliers to find the maximum value of the function subject to the given constraints.

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Find Find for . for Find for . .

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Find and classify the relative extrema and saddle points of the function Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None for Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None and Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None .


A) Relative maximum Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None
B) Saddle point Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None
C) Relative minimum Find and classify the relative extrema and saddle points of the function for and . A) Relative maximum B) Saddle point C) Relative minimum D) None
D) None

E) A) and B)
F) All of the above

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Find the differential of the function Find the differential of the function

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Find Find for the function A) B) C) D) for the function Find for the function A) B) C) D)


A) Find for the function A) B) C) D)
B) Find for the function A) B) C) D)
C) Find for the function A) B) C) D)
D) Find for the function A) B) C) D)

E) B) and C)
F) A) and B)

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Describe the level surfaces of the function Describe the level surfaces of the function . .

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A family o...

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If If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E) use the gradient vector If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E) to find the tangent line to the level curve If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E) at the point If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E) .


A) If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E)
B) If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E)
C) If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E)
D) If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E)
E) If use the gradient vector to find the tangent line to the level curve at the point . A) B) C) D) E)

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

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Find the directional derivative of the function Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis. A) 1 B) C) D) 11 at the point Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis. A) 1 B) C) D) 11 in the direction of the unit vector that makes the angle Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis. A) 1 B) C) D) 11 with the positive x-axis.


A) 1
B) Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis. A) 1 B) C) D) 11
C) Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis. A) 1 B) C) D) 11
D) 11

E) A) and B)
F) A) and C)

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Find the limit Find the limit A) B) C) D)


A) Find the limit A) B) C) D)
B) Find the limit A) B) C) D)
C) Find the limit A) B) C) D)
D) Find the limit A) B) C) D)

E) A) and D)
F) None of the above

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Find the equation of the tangent plane to the given surface at the specified point. Find the equation of the tangent plane to the given surface at the specified point.

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Describe the level survaces of the function Describe the level survaces of the function . .

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A family o...

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Find the dimensions of the rectangular box with largest volume if the total surface area is given as Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm .


A) Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, 1.75 cm
B) Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, 1.75 cm, 1.75 cm
C) Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm,
Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm
D) Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm,
Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm
E) Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, Find the dimensions of the rectangular box with largest volume if the total surface area is given as . A) cm, cm, 1.75 cm B) cm, 1.75 cm, 1.75 cm C) cm, cm, cm D) cm, cm, cm E) cm, cm, 3.5 cm cm, 3.5 cm

F) D) and E)
G) B) and C)

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The ellipsoid The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E) intersects the plane The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E) in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) .


A) The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E)
B) The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E)
C) The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E)
D) The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E)
E) The ellipsoid intersects the plane in an ellipse. Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2) . A) B) C) D) E)

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

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Find Find , if and . , if Find , if and . and Find , if and . .

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