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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. Calculate the flux of a vector field F = over S, where S is the boundary of the unit sphere.
2. Use the properties of the double integrals

and

to evaluate

.
3. Find
, if
.
4. Find the linear acceleration for the curve given by r(t)= < cost, sint >.
5. Find the acceleration of the following function 'font-weight:bold;'>x(t) = 3,t2,t2>.
6. Find the vector
with initial point 'font-style:italic;'>P1 (-1,-3) and final point 'font-style:italic;'>P2 (0,2).
7. Evaluate
.
8. Fubini's theorem does NOT apply to
because of which reason?
9. Which of the following statements is true of f(x,y)= x+y?
10. Suppose f and g are continuous at point (a, b), then which of the following functions is also continuous?
11. Using Fubini's theorem, calculate

, where R = [0, 1] x [0, 1].
12. 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.
13. Calculate the surface area of the partxy + z that is in the plane x + y + z = 2 in the first octant.
14. 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.
15. Determine where the function
is continuous?
16. What is
?
17. Use Lagrange Multipliers to find the maximum of f(x,y) = 4xy subject to the constraint x2+y2=1.
18. Find the unit normal 'font-style:italic;font-weight:bold;'>N'font-style:italic;'>(t) for the curve given by 'font-style:italic;'>'font-weight:bold;'>r(t)= <-2'font-style:italic;'>t,-'font-style:italic;'>t2>.
19. Suppose a vector field F represents the velocity of a fluid through a membrane represented by S.What does the flux represent?
20. Let
and
be vectors, then what is
?
21. Evaluate

, where C is the right half of the circle parameterized by x=3 cos⁡(t),y=3 sin(t) for t in
22. The directional derivative, given by
, provides which of the following?
23. 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.
24. Fill in the blank. The domain of the function
is __________.
25. Use Green's theorem to evaluate
, where R is a unit square.

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