Name:
Final Exam/MAC2313 Page 1 of 7
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STUDENT #:
EXAM #:
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Read Me First
:
Read each problem carefully and do exactly what is requested.
Full credit will be awarded only if
you show all your work neatly, and it is correct.
Use complete sentences and use notation correctly.
Remember that what is illegible or incomprehensible is worthless.
Communicate.
Eschew obfuscation.
Good Luck!
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1. (12 pts.)
Evaluate the iterated integral by reversing the order of
integration.
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2. (18 pts.) (a) Obtain an equation for the plane that is tangent to the
graph of the function
at the point (1,2,5) in 3space.
(b) Consider the function f of three variables defined by
Obtain an equation for the level surface for this function that passes
through the point (1,1, 1) in 3space.
(c) Obtain an equation for the plane that is tangent to the level surface
given in part (b) with the point of tangency being (1,1, 1).
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Final Exam/MAC2313 Page 2 of 7
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3. (12 pts.) Obtain an arclength parameterization for the curve
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 Spring '06
 GRANTCHAROV
 Multivariable Calculus, pts, Line integral, Stokes' theorem

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