
Limits and Continuity in Multivariable Functions

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

Patricia Brown
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the limit of the function as (x, y) approaches (0, 0) along the x-axis?
0
1
Does not exist
2
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why does the limit not exist when approaching (0, 0) along different paths?
The function is undefined
Different paths yield different results
The function is continuous
The function is a polynomial
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the result of the limit as (x, y) approaches (0, 0) using the path y = 2x?
1
0
-1
2
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is necessary to conclude that a limit equals zero?
Algebraic simplification
Trying multiple paths
Using a polynomial
Checking continuity
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the limit of the function as (x, y) approaches (0, 0) along the line y = x?
1/2
1
Does not exist
0
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can you determine if a limit exists for a continuous function?
By checking different paths
By plugging in values
By using derivatives
By graphing the function
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What happens when you encounter a 0/0 situation in a limit problem?
The limit does not exist
The function is continuous
Algebraic simplification may help
The function is undefined
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