
Differentials and Partial Derivatives
Interactive Video
•
Mathematics
•
11th Grade - University
•
Practice Problem
•
Hard
Olivia Brooks
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the total differential of a function of two variables?
The sum of the derivatives of the function with respect to each variable.
The product of the derivatives of the function with respect to each variable.
The sum of the partial derivatives of the function with respect to each variable, each multiplied by the change in that variable.
The difference between the partial derivatives of the function with respect to each variable.
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How can differentials be used in calculus?
To approximate the change in a function when variables change.
To determine the maximum value of a function.
To solve differential equations.
To find the exact value of a function.
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the first step in calculating the total differential of a function?
Finding the limit of the function.
Calculating the integral of the function.
Determining the partial derivatives of the function.
Finding the second derivative of the function.
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the purpose of rewriting the function as X squared plus Y squared raised to the 1/2 power?
To simplify the calculation of partial derivatives.
To make the function easier to integrate.
To solve the function for specific values of X and Y.
To find the maximum value of the function.
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
When calculating differential Z, what is the role of partial derivatives?
They are used to solve the function for a specific value.
They are used to determine the rate of change of the function with respect to each variable.
They are used to find the maximum and minimum values of the function.
They are used to integrate the function over a given interval.
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the significance of the comparison between differential Z and delta Z?
It proves that delta Z is more accurate than differential Z.
It shows that differential Z is always greater than delta Z.
It highlights that differential Z can be a good approximation of delta Z.
It demonstrates that differential Z is a perfect approximation of delta Z.
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
In the context of differentials, what does DX represent?
The integral of X over a given interval.
The change in the variable X.
The derivative of X with respect to time.
The maximum value of X.
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