What is the shape of the solid bounded by the equation x^2 + y^2 + z^2 = 25 and x = 0?

Understanding the Divergence Theorem and Flux

Interactive Video
•
Mathematics, Physics, Science
•
11th Grade - University
•
Hard

Emma Peterson
FREE Resource
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10 questions
Show all answers
1.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
A cylinder
A full sphere
A hemisphere
A cube
2.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
Which theorem is used to compute the outward flux across a surface?
Stokes' Theorem
Green's Theorem
Divergence Theorem
Pythagorean Theorem
3.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What must be true about the partial derivatives for the Divergence Theorem to apply?
They must be zero
They must be continuous
They must be positive
They must be negative
4.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the x-component of the vector field in the given problem?
5 - 2xyz
3z - x^2z
x^2z
x^2 + y^2
5.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the z-component of the vector field in the given problem?
5 - 2xyz
x^2z
3z - x^2z
x^2 + y^2
6.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
How do you find the divergence of a vector field?
By taking the cross product of the vector field
By subtracting the partial derivatives of its components
By summing the partial derivatives of its components
By integrating the vector field
7.
MULTIPLE CHOICE QUESTION
30 sec • 1 pt
What is the divergence of the vector field in this problem?
2xz + 2xz + 3 - 3 + x^2 + x^2
5
2xz - 2xz - 3 + 3 + x^2 - x^2
0
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