136.272
Assignment 1 (Sections 13.1-13.7, 14.1-14.2) Solutions
1. [5 marks] Find the equation of the plane which contains the point (3,1,5) and is
perpendicular to the intersection of the planes x 5y + 2z = 3 and 4 x + y z = 2 .
Solution.
Before we start
136.272
Assignment 3 Brief Solutions
1. [4 marks].
(a) [2] Find f x (0,0) and find f y (x, y) if f (x, y) = e xy sin(x + y + ) .
(b) [2] Find all (four) second order partial derivatives of g(x, y) = xy 2 + ln(x + y) .
Solution.
[2] (a) f x (x, y) = ye xy
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THE UNIVERSITY OF MANITOBA
DATE: Oct. 26, 2005
MIDTERM EXAMINATION
DEPARTMENT & COURSE NO: 136.272
TIME: 1 hour
EXAMINATION: Calculus 3A
EXAMINER: Dr. S.Kalajdzievski
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NAME: (PRINT)_
STUDENT NUMBER:_
SIGNATURE:_
(I understand that cheating is a serious
136.272 Solutions
Assignment 4 (Sections 16.1-16.4)
1. [6 marks] Use the method of Lagrange multipliers to find and classify the extrema of
the function f (x, y) = xy subject to the constraint x 2 + y 2 4 = 0 .
Solution. Denote F(x, y, ) = f (x, y) + ( x
136.272
Assignment 2 (Sections 14.3, 14.4, 15.1-15.2)
Posted: Oct.17 2005; handed Oct. 20, 2005. Due: Oct.24 2005 in class. (If you hand it in
by Friday, Oct 21, you will get it back before the midterm.) Late assignments will not be
accepted.
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