
Understanding Limits of Functions of Two Variables

Interactive Video
•
Mathematics
•
10th - 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 condition for the limit of a function of two variables to exist at a point?
The function must be zero at that point.
The function must be integrable at that point.
The limit must be the same from all paths approaching the point.
The function must be differentiable at that point.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why is continuity important when finding limits using direct substitution?
It ensures the function is differentiable.
It allows the limit to be found without considering all paths.
It guarantees the function is bounded.
It makes the function periodic.
Tags
CCSS.HSF.LE.A.2
CCSS.8.F.B.4
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the first example, what is the limit of the function as x, y approaches 2, 1?
3
4
5
6
Tags
CCSS.HSF.LE.A.2
CCSS.8.F.B.4
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function used in the first example?
x^2 + 2y
2x + y^2
x + 2y^2
x + y^2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the second example, what is the limit of the rational function as x, y approaches 2, 1?
1/2
5/6
2/3
4/9
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Why can direct substitution be used in the second example?
The function is continuous at the point.
The function is periodic at the point.
The function is differentiable at the point.
The function is zero at the point.
Tags
CCSS.HSF-IF.C.7D
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What would be the issue if the function approached the point (0, 0) in the second example?
The function would have an indeterminate form.
The function would be differentiable.
The function would be continuous.
The function would be undefined.
Tags
CCSS.HSF-IF.C.7D
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