136.270
Assignment 3 (Sections 14.4, 14.5, 14.6)
Solutions
1. [5 marks] [2](a) Find
and z = cosu .
v2
w
when u = 1 and v = 2 if w = xy + ln z , x = , y = u + v
u
v
z
z
and
at the point (1,1,1) if z is the function on x and y
y
x
defined by the equation z
136.270 Solutions Assignment 4 (Sections 16.1-16.4)
1. [8 marks] Evaluate
2
(4 xy
D
3
- 4 x 2 y ) dA where D is the region bounded by
y = - 1 - x , y = 1 - x and y = 1 + x . Sketch D.
Solution. The parabolas y = 1 - x and y = 1 + x intersect at the point
136.270 Assignment 2 (Sections 14.3, 15.1-15.3)
Handed: Oct.10 2003. Due: Oct.17 2003 in class. Show your work; providing answers without justifying them would not be sufficient.
r 1. [8 marks] A spiral curve is defined by the vector function r ( t ) = (
136.270 Assignment 3 Brief Solutions
1. [5 marks] (a) Find the directional derivative of the function f ( x, y ) =
x2 - y2 in the x2 + y2
1 1 direction of the unit vector u = , at the point (1,-2). 2 2 (b) Find the directions and the values of the smalles
1 THE UNIVERSITY OF MANITOBA DATE: Oct. 22, 2002 DEPARTMENT & COURSE NO: 136.270 MIDTERM EXAMINATION TIME: 1 hour
EXAMINATION: Calculus 3A EXAMINER: Dr. F. Ghahramani _ NAME: (PRINT)_ STUDENT NUMBER:_ SIGNATURE:_ (I understand that cheating is a serious o
136.270 Assignment 1 (Sections 13.1-13.7, 14.1-14.2) Solutions
Handed: Sept. 24 2003. Due: Oct.1 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 - 5 y + 2 z = 3 and
1111:... v.55; l-I'I'I-lI-l I VI. l
DEPARTMENT & CDURSE NE: W TIME: 2 HIDURS
EHAM [NAHUM W WHERE: W
31111::
[12] 1. Find an equaun ufmtmgmtplnnnn :11: smaller g]: 3H; at {4,2,3}.
[6] 2. [3} Suppose Hug] has mmimmu punial den-mum. Find
ghummmu] in Imus
136.270 Solutions
Assignment 4 (Sections 14.7, 14.8, 15.1, 15.2, 15.3)
Handed: November 24, 2004. Due: December 1, 2004 in class.
Show your work. Providing answers without justifying them will not be sufficient.
1.
An open-top rectangular box of a specifi
136.270 Solutions
Assignment 1 (Sections 13.1-13.7, 14.1-14.2)
Handed: October 4, 2004. Due: October 13, 2004 in
1. [6 marks] Find parametric equations of the line through the point (0,1,2), that is
perpendicular to the line x = 1 + t,y = 1 t,z = 2t and i
1
THE UNIVERSITY OF MANITOBA
DATE: Oct. 27, 2004
MIDTERM EXAMINATION
DEPARTMENT & COURSE NO: 136.270
TIME: 1 hour
EXAMINATION: Calculus 3A
EXAMINER: Dr. S.Kalajdzievski
_
NAME: (PRINT)_
STUDENT NUMBER:_
SIGNATURE:_
(I understand that cheating is a serious
1 THE UNIVERSITY OF MANITOBA DATE: Oct. 22, 2001 DEPARTMENT & COURSE NO: 136.270 MIDTERM EXAMINATION TIME: 1 hour
EXAMINATION: Calculus 3A EXAMINER: Dr. F. Ghahramani _ NAME: (PRINT)_ STUDENT NUMBER:_ SIGNATURE:_ (I understand that cheating is a serious o