
Partial Derivatives Quiz
Quiz
•
Mathematics
•
12th Grade
•
Practice Problem
•
Medium
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5 questions
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1.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
The temperature T at a location in the Northern Hemisphere depends on longitude x, latitude y, and time t, so we can write T= f(x,y,t). The time is measured since January 1.
What is the meaning of the partial derivatives dT/dx?
The rate of change of temperature with respect to time
The rate of change of the time with respect to temperature
The rate of change of temperature as longitude and time varies
The rate of change of temperature as longitude varies with latitude and time fixed
2.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Define a two-variable function as follows: f(x, y) = x2 + 2xy + y2
∂f/dx = _______
2x + 2y
2x + 2y + 2x(dy/dx) + 2y(dy/dx)
4y
df/dx + 2xy
3.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
Let f(a,b,c) = cos(ab) sin(b)+c
where f(1/2, π/3, 7)
Evaluate ∂f/∂a (1/2 ,π/3, 7)
π/3
-π/3
-π(sqrt(3)) / 12
π/24 / sqrt(3)
4.
MULTIPLE CHOICE QUESTION
2 mins • 1 pt
What can we informally define partial derivatives graphically?
A constant always
The 2D slope of the slice of a 3D graph
The derivative of the whole thing
The 3D derivative
5.
MULTIPLE CHOICE QUESTION
5 mins • 1 pt
z= (2x + 3y)10
Which is the correct partial derivative?
z' = 60 (dy/dx) (2 + 3y)9
fx= 20 (2x + 3y)9
fy= 20 (2x + 3y)9
fz= 30 (2x)9
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