UNIVERSITY OF WINNIPEG
1 April 2013
Assignment #5
TOTAL PAGES: 1
COURSE: MATH 2106, Intermediate Calc II
TOTAL MARKS: 50
DUE: 5 April 2013 at 2:30pm
1
[10]Q.1 Reverse the order of integration in the double integral
x
xdydx. Evaluate the
0
resulting integr
MATH 153
Selected Solutions for 12.5
Exercise 34: Find an equation for the plane that passes through the point
(6, 0, 2) and contains the line x = 3t, y = 1 + t, z = 7 + 4t.
Solution: In order to nd the equation for a plane, we need a point in the
plane a
Multivariable Calculus Practice Midterm 2
Prof. Fedorchuk
1.
(10 points ) Compute the arc length of the curve
r(t) =
43
t, t 2 , t2 ,
3
on the interval 1 t 3.
1
Solution: We have r (t) = 1, 2t 2 , 2t and r (t) =
arc length is
1 + 4t + 4t2 = 1 + 2t. Hence
SOLUTIONS TO HOMEWORK ASSIGNMENT #2, Math 253
1. Find the equation of a sphere if one of its diameters has end points (1, 0, 5) and
(5, 4, 7).
Solution:
The length of the diameter is (5 1)2 + (4 0)2 + (7 5)2 = 36 = 6, so the
radius is 3. The centre is at
UNIVERSITY OF WINNIPEG
21 January 2013
Assignment #1
TOTAL PAGES: 1
COURSE: MATH 2106, Intermediate Calc II
TOTAL MARKS: 50
DUE: 25 January 2013 at 2:30pm
[5]Q.1 For two vectors u and v in R3 , show that
(u v) tan = u v
where is the angle between u and v.
UNIVERSITY OF WINNIPEG
4 March 2013
Assignment #4
TOTAL PAGES: 1
COURSE: MATH 2106, Intermediate Calc II
TOTAL MARKS: 50
DUE: 8 March 2013 at 2:30pm
2
[5]Q.1 If z = f (x, y), where x = r cos and y = r sin , nd z .
r
[10]Q.2 Show that the ellipsoid 3x2 +2y
MATH-2106 WINTER 2014 INTERMEDIATE CALCULUS II Page 11
Cross Product of Vectors in R3
Denition: 7
Let a : (a1,a2,a3) and b m (bl, 62,53) he vectors in R3, then the cross product of a
and b is the sector
a X b = (a2b3 (1352501351 _ (1153,3le (12131),
UNIVERSITY OF WINNIPEG
1 February 2013
Assignment #2
TOTAL PAGES: 2
COURSE: MATH 2106, Intermediate Calc II
TOTAL MARKS: 50
DUE: 8 February 2013 at 2:30pm
[5]Q.1 For each part (a) - (c), nd a multivariable function whose domain is given.
(a) All the point