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MA103 Final Exam - Multivariable Calculus
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MCQs on Multivariable Calculus.

MA103 Final Exam - Multivariable Calculus
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25 Questions

1. What is the definition of the surface area differential for a surface S?
2. The directional derivative, given by
, provides which of the following?
3. Which of the following statements is true of f(x,y)= x+y?
4. Find
X
.
5. Fill in the blank. The domain of the function
is ____________.
6. Which of the following is a Type I integral?
7. Suppose a vector field F represents the velocity of a fluid through a membrane represented by S.What does the flux represent?
8. Using Fubini's theorem, calculate

, where R = [0, 1] x [0, 1].
9. Find the angle in degrees between vectors
and
.
10. Find the volume of a solid between z=x and z=x-y over R: y = 0 and y = 1 and x = y3 and x = y.
11. Use Green's theorem to find the area of a disk of radius 2.
12. Find the gradient vector field of U(x,y)= -x2-y2.
13. Choose the best answers to fill in the blanks. If
is the gradient of some function
, then
is called a _____________, and function
is said to be a ______________ for
.
14. Find the unit tangent vector to the curve
.
15. Find the center of mass of the lamina of the unit square with mass density m(x,y)=(x+y) kg/m2.
16. If F(x,y,z) and G(x,y,z) are differentiable in each component, then which of the following is true?
17. Use Lagrange Multipliers to find the maximum of f(x,y) = 4xy subject to the constraint x2+y2=1.
18. Calculate the surface area of sphere of radius R.
19. Apply Stokes' theorem to evaluate the appropriate integral. Let C be the circle of radius R centered at the origin, and let F = -y3 i+x3j be the vector field.
20. Calculate the flux of F over S, where F is the vector field and S is the boundary of the region enclosed by the paraboloid z=1-x2-y2 and the plane z=0.
21. Fill in the blank. If div(V)=0, then there exists a vector field W such that _______________.
22. What is the definition of the partial derivative of f(x,y) with respect to x?
23. If a solid has a mass density of m(x,y,z), then what is the total gravitational potential energy of the solid?
24. Fill in the blank. The vector field
is ___________.
25. Choose the best answer to fill in the blanks. If
, then
and
are _____________ vectors, and if
, then
is _____________ to both
and
.

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