Deck 15: Partial Derivatives

Question 1

Find the domain and range and describe the level curves for the function f(x,y).
f(x, y) = -6x + 8y

Answer 1

B

Question 2

Find the specific function value.

A) 108
B) -72
C) -49
D) -54

Answer 2

D

Question 3

Find the domain and range and describe the level curves for the function f(x,y).

Answer 3

D

Question 4

Match the surface show below to the graph of its level curves.

Question 5

Match the surface show below to the graph of its level curves.

Question 6

Find the specific function value.

A) -302
B) -310
C) -232
D) -237

Question 7

Find the specific function value.
Find f(-3, 6) when f(x, y) = 5x + 2y - 3.

A) -3
B) -6
C) -11
D) -8

Question 8

Find the domain and range and describe the level curves for the function f(x,y).

Question 9

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

Question 10

Find the specific function value.

Question 11

Find the specific function value.

Question 12

Find the specific function value.
Find f(100, 3) when f(x, y) = y log x.

A) 3
B) 60
C) 6
D) 30

Question 13

Find the domain and range and describe the level curves for the function f(x,y).

Question 14

Find the specific function value.

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

Question 15

Find the specific function value.

A) 100
B) 1000
C) 30
D) 280

Question 16

Find the domain and range and describe the level curves for the function f(x,y).

Question 17

Find the domain and range and describe the level curves for the function f(x,y).

Question 18

Find the domain and range and describe the level curves for the function f(x,y).
f(x, y) = ln (5x + 4y)

Question 19

Find the domain and range and describe the level curves for the function f(x,y).

Question 20

Find the domain and range and describe the level curves for the function f(x,y).

Question 21

Match the surface show below to the graph of its level curves.

Question 22

Sketch the surface z = f(x,y).

Question 23

Match the surface show below to the graph of its level curves.

Question 24

Sketch the surface z = f(x,y).

Question 25

Match the surface show below to the graph of its level curves.

Question 26

Sketch the surface z = f(x,y).

Question 27

Solve the problem.

Question 28

Sketch the surface z = f(x,y).

Question 29

Sketch the surface z = f(x,y).

Question 30

Match the surface show below to the graph of its level curves.

Question 31

Match the surface show below to the graph of its level curves.

Question 32

Sketch the surface z = f(x,y).

Question 33

Sketch the surface z = f(x,y).

Question 34

Solve the problem.

Question 35

Solve the problem.

Question 36

Match the surface show below to the graph of its level curves.

Question 37

Sketch the surface z = f(x,y).

Question 38

Sketch the surface z = f(x,y).

Question 39

Solve the problem.

Question 40

Sketch the surface z = f(x,y).

Question 41

Find the equation for the level surface of the function through the given point.

Question 42

Solve the problem.

Question 43

Solve the problem.

Question 44

Sketch a typical level surface for the function.

Question 45

Solve the problem.

Question 46

Sketch a typical level surface for the function.

Question 47

Sketch a typical level surface for the function.

Question 48

Find the equation for the level surface of the function through the given point.

Question 49

Find the equation for the level surface of the function through the given point.

Question 50

Find the equation for the level surface of the function through the given point.

Question 51

Solve the problem.

Question 52

Sketch a typical level surface for the function.

Question 53

Sketch a typical level surface for the function.

Question 54

Provide an appropriate response.

Question 55

Provide an appropriate response.
Find the extrema of f(x, y, z) = x + yz on the line defined by x = 8(6 + t), y = t - 8, and z = t + 6. Classify each extremum as a minimum or maximum. (Hint: w = f(x, y, z) is a differentiable function of t.)

A) (24, -11, 3), minimum
B) (72, -5, 9), minimum; (0, -8, 0), minimum
C) (24, -11, 3), minimum; (72, -5, 9), maximum
D) (72, -5, 9), minimum

Question 56

Sketch a typical level surface for the function.

Question 57

Solve the problem.

Question 58

Provide an appropriate response.

Question 59

Sketch a typical level surface for the function.

Question 60

Solve the problem.

Question 61

Find the limit.

Question 62

Find the limit.

Question 63

Find the limit.

A) 8
B) 4
C) 0
D) No limit

Question 64

Find the limit.

A) 16
B) 4
C) - 4
D) No limit

Question 65

Find the limit.

Question 66

Find the limit.

A) 4
B) 0
C) 12
D) 1

Question 67

Find the limit.

A) -ln 2
B) ln 2
C) 0
D) No limit

Question 68

Find the limit.

Question 69

Find the limit.

A) 16
B) 0
C) 8
D) No limit

Question 70

Find the limit.

Question 71

Find the limit.

A) ln 81
B) ln (3) - 4
C) 81
D) No limit

Question 72

Find the limit.

Question 73

Find the limit.

A) 6
B) - 3
C) -7
D) 7

Question 74

Find the limit.

Question 75

Find the limit.

Question 76

Find the limit.

Question 77

Find the limit.

Question 78

Find the limit.

A) 9
B) 8
C) 2
D) 1

Question 79

Find the limit.

Question 80

Find the limit.