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Determine the largest set on which the function is continuous. Determine the largest set on which the function is continuous.

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Determine where the function Determine where the function is continuous. is continuous.

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Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32


A) Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32 , Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32 ,
Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32
B) 4, 8, 16
C) 32, Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32 , 16
D) Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32 , Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32 ,
Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is A) , , B) 4, 8, 16 C) 32, , 16 D) , , E) 32, 32, 32
E) 32, 32, 32

F) D) and E)
G) A) and E)

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Find the first partial derivatives of the function Find the first partial derivatives of the function

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A cardboard box without a lid is to have a volume of A cardboard box without a lid is to have a volume of cm . Find the dimensions that minimize the amount of cardboard used. cm A cardboard box without a lid is to have a volume of cm . Find the dimensions that minimize the amount of cardboard used. . Find the dimensions that minimize the amount of cardboard used.

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


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

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

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Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)


A) Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)
B) Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)
C) Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)
D) Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)
E) Use Lagrange multipliers to find the maximum value of the function subject to the given constraint. A) B) C) D) E)

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

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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. A) B) C) D) E)


A) Find the equation of the tangent plane to the given surface at the specified point. A) B) C) D) E)
B) Find the equation of the tangent plane to the given surface at the specified point. A) B) C) D) E)
C) Find the equation of the tangent plane to the given surface at the specified point. A) B) C) D) E)
D) Find the equation of the tangent plane to the given surface at the specified point. A) B) C) D) E)
E) Find the equation of the tangent plane to the given surface at the specified point. A) B) C) D) E)

F) B) and C)
G) None of the above

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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 . .

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Relative m...

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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) None of the above
G) A) and B)

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Use partial derivatives to find the implicit derivative Use partial derivatives to find the implicit derivative Use partial derivatives to find the implicit derivative

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Find all the second partial derivatives. Find all the second partial derivatives.

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Find equations for the tangent plane and the normal line to the surface with equation Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) , at the point Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) ,


A) Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) , , Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) ,
B) Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) , , Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) ,
C) Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) , , Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) ,
D) Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) , , Find equations for the tangent plane and the normal line to the surface with equation at the point A) , B) , C) , D) ,

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

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Two contour maps are shown. One is for a function f whose graph is a cone. The other is for a function g whose graph is a paraboloid. Which is the contour map of a cone? Two contour maps are shown. One is for a function f whose graph is a cone. The other is for a function g whose graph is a paraboloid. Which is the contour map of a cone? A) impossible to determine B) II C) I


A) impossible to determine
B) II
C) I

D) None of the above
E) All of the above

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Evaluate the limit. Evaluate the limit. A) 0 B) the limit does not exist C) D) 1 E) 2


A) 0
B) the limit does not exist
C) Evaluate the limit. A) 0 B) the limit does not exist C) D) 1 E) 2
D) 1
E) 2

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

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Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.)


A) 6.91 Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7
B) 6.99 Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7
C) Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7 Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7
D) 8.34 Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7
E) 6.7 Use differentials to estimate the amount of metal in a closed cylindrical can that is 12 cm high and 8 cm in diameter if the metal in the top and bottom is 0.09 cm thick and the metal in the sides is 0.01 cm thick. (rounded to the nearest hundredth.) A) 6.91 B) 6.99 C) D) 8.34 E) 6.7

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

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Find the differential of the function Find the differential of the function A) B) C) D)


A) Find the differential of the function A) B) C) D)
B) Find the differential of the function A) B) C) D)
C) Find the differential of the function A) B) C) D)
D) Find the differential of the function A) B) C) D)

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

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


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

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

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Find Find . . Find .

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Find the limit. Find the limit.

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