[ph 2-] as a function of Time
0
0
0
[ph 2-] (M)
0
0
0
21.0
36.0
54.0
72.0
90.0
108.0
Time (s)
126.0
144.0
162.0
180.0
Run 6 (fast run)
ln[ph 2-] as a function of Time
-9.5
21.0
36.0
54.0
72.0
90.0
108.0
-10
-10.5
-11
ln[ph 2-] (M)
-11.5
-12
-12.5
-13
Time
COURSE OUTLINE
Winter 2017
Date
Initials
Prepared by Instructor
Approved by Head
1. Calendar Information
ENGG 202 Engineering Statics
Force vectors; equilibrium of a particle in two and three dimensions; force system
resultants; equilibrium of a rigid bod
Problem
Score
1
2
Name:
3
SID:
4
Section:
5
Instructor:
6
7
8
9
10
11
12
Total
MATH 230 FALL 2004
FINAL EXAM
DECEMBER 13, 2004 12:20-2:10 PM
INSTRUCTIONS
There are 12 problems on this exam for a total of 150 points. Some problems
have multiple parts.
PL
EXAM I, FALL 2010SOLUTIONS
Problem 1. (10 points)
Vectors u and v have length 1. Which of the assumptions (a)(g) below
imply that vectors u and v are
(i)
perpendicular
(ii)
parallel and pointing in the same direction
(iii) parallel and pointing in the opp
Final Exam
Calculus III
8 May, 2009
Name:
Student ID Number:
Instructor:
Section:
The use of a calculator, cell phone, or any other electronic device is not permitted for
this examination.
The use of notes of any kind is not permitted during this examinat
Exam 2, Fall 2010Solutions
Problem 1. (10 points)
Let f (x, y ) = 2e2xy + 2.
(a) (4 pts) Find the linearization of the function f at the point (5, 10).
Solution: The linearization L(x, y ) of f (x, y ) at P = (x0 , y0 ) is dened by
L(x, y ) = f (P ) + fx
Answers to Sample A
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
2.
3.
4.
5.
6.
7.
Absolute minimum 0 at (0, 0). Absolute maximum 8 at (0, 2) and (0, 2).
R
R
(1, 2) = 8,
(1, 2) = 2.
u
v
(a) f is increasing fastest in the direction of 1/ 10, 3/ 10 . (b) (0, 0).
(e4 1)
.
Midterm Exam I, Calculus III, Sample A
1. (10 points) Show that the 4 points P1 = (0, 0, 0), P2 = (2, 3, 0), P3 = (1, 1, 1), P4 = (1, 4, 1) are coplanar (they lie on the same plane), and nd the equation of the plane that contains them. Solution: u = P1 P2
Midterm Exam I, Calculus III, Sample A
1. (10 points) Show that the 4 points P1 = (0, 0, 0), P2 = (2, 3, 0), P3 = (1, 1, 1), P4 = (1, 4, 1) are coplanar (they lie on the same plane), and nd the equation of the plane that contains them. 2. (10 points) Find