
Understanding Limits in Multivariable Calculus

Interactive Video
•
Mathematics
•
10th - 12th Grade
•
Hard
Standards-aligned

Ethan Morris
Used 1+ times
FREE Resource
Standards-aligned
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function whose limit we are trying to find as (x, y) approaches (0, 0)?
9xy / (6x^2 + y^2)
9x^2 / (6xy + y^2)
6x^2 / (9xy + y^2)
6xy / (9x^2 + y^2)
Tags
CCSS.HSF-IF.C.7A
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What must be true for a general limit to exist in multivariable calculus?
The limit must be the same from all paths.
The limit must be undefined.
The limit must be zero.
The limit must be infinite.
Tags
CCSS.HSF-IF.C.7A
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the graph in three dimensions in this context?
It proves the function is continuous.
It helps visualize the different paths and their limits.
It shows the function is linear.
It demonstrates the function is quadratic.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is made to find the limit along the path y = x?
Substitute x = -y
Substitute y = 2x
Substitute x = y
Substitute y = x
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the simplified limit along the path y = x?
1/2
6/10
3/5
2/3
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the function value along the path y = x as we approach (0, 0)?
Below the XY plane
Undefined
Above the XY plane
On the XY plane
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What substitution is made to find the limit along the path y = -2x?
Substitute y = -2x
Substitute y = 2x
Substitute x = -2y
Substitute x = 2y
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