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Solve the problem. -Solve the problem. -  A)  -0.03 watts B)  0.13 watts C)  -0.13 watts D)  0.03 watts


A) -0.03 watts
B) 0.13 watts
C) -0.13 watts
D) 0.03 watts

E) None of the above
F) All of the above

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Match the surface show below to the graph of its level curves. -Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)


A)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
B)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
C)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
D)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)

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

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Find all the first order partial derivatives for the following function. -f(x ,y, z) = (sin xy) (cos y Find all the first order partial derivatives for the following function.   -f(x ,y, z)  = (sin xy) (cos y   )  A)     B)    C)    D)    )


A)
Find all the first order partial derivatives for the following function.   -f(x ,y, z)  = (sin xy) (cos y   )  A)     B)    C)    D)
B) Find all the first order partial derivatives for the following function.   -f(x ,y, z)  = (sin xy) (cos y   )  A)     B)    C)    D)
C) Find all the first order partial derivatives for the following function.   -f(x ,y, z)  = (sin xy) (cos y   )  A)     B)    C)    D)
D) Find all the first order partial derivatives for the following function.   -f(x ,y, z)  = (sin xy) (cos y   )  A)     B)    C)    D)

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

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Find all the first order partial derivatives for the following function. -f(x, y, z) = cos x Find all the first order partial derivatives for the following function.   -f(x, y, z)  = cos x   yz A)      B)     C)      D)    yz


A) Find all the first order partial derivatives for the following function.   -f(x, y, z)  = cos x   yz A)      B)     C)      D)
B) Find all the first order partial derivatives for the following function.   -f(x, y, z)  = cos x   yz A)      B)     C)      D)
C) Find all the first order partial derivatives for the following function.   -f(x, y, z)  = cos x   yz A)      B)     C)      D)
D) Find all the first order partial derivatives for the following function.   -f(x, y, z)  = cos x   yz A)      B)     C)      D)

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

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Find the domain and range and describe the level curves for the function f(x,y) . -f(x, y) = Find the domain and range and describe the level curves for the function f(x,y) . -f(x, y)  =   A)   Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c    B)   Domain: all points in the first quadrant of the xy-plane; range: real numbers z > 0; level curves: lines x + y = c    C)   Domain: all points in the xy-plane; range: real numbers z > 0; level curves: lines x + y = c    D)   Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c


A) Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c

B) Domain: all points in the first quadrant of the xy-plane; range: real numbers z > 0; level curves: lines x + y = c

C) Domain: all points in the xy-plane; range: real numbers z > 0; level curves: lines x + y = c

D) Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c

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

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Match the surface show below to the graph of its level curves. -Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)


A)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
B)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
C)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)
D)
Match the surface show below to the graph of its level curves. -  A)     B)     C)     D)

E) None of the above
F) All of the above

Correct Answer

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Sketch the surface z = f(x,y) . -f(x, y) = 4 Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)    + 4 Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)    + 2


A)
Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)
B)
Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)
C)
Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)
D)
Sketch the surface z = f(x,y) . -f(x, y)  = 4   + 4   + 2 A)     B)     C)     D)

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

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Solve the problem. -Find the point on the sphere Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)   that is closest to the point Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)


A) Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)
B) Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)
C) Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)
D) Solve the problem. -Find the point on the sphere   that is closest to the point   A)    B)    C)    D)

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

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Find the limit. -Find the limit. -    x -   y + z A)  8 B)  9 C)  6 D)  7 Find the limit. -    x -   y + z A)  8 B)  9 C)  6 D)  7 x - Find the limit. -    x -   y + z A)  8 B)  9 C)  6 D)  7 y + z


A) 8
B) 9
C) 6
D) 7

E) None of the above
F) All of the above

Correct Answer

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