
Understanding the Average Value of a Function of Two Variables

Interactive Video
•
Mathematics
•
11th - 12th Grade
•
Hard
Standards-aligned

Jackson Turner
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the average value of a function of two variables interpreted as?
The total area under the curve
The average height of the surface over a region
The maximum value of the function
The minimum value of the function
Tags
CCSS.HSF-IF.C.7E
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the example problem, what is the function being evaluated?
x^2 + y^2
e^(x+y)
e^(x-y)
x + y
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the area of the region over which the function is integrated in the example?
2
3
5
4
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
During the integration process, what is the first variable with respect to which integration is performed?
t
z
x
y
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the integration with respect to x before evaluating the limits?
e^(x) - e^(y)
e^(y) - e^(x)
e^(x+y) - e^(x)
e^(2+y) - e^(0+y)
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the approximate average height of the surface over the region?
10.2
20.4
15.3
5.1
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What does the value 40.82 represent in the context of the example?
The average height of the surface
The total area of the region
The maximum value of the function
The approximate volume above the XY plane
Tags
CCSS.8.F.A.1
CCSS.HSF.IF.B.5
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