MAT1332A - Calculus for the Life Sciences II - Fall 2009
Assignment 3 This assignment is worth a total of 50 points. Due on Thursday, November 19, at the beginning of the lecture. Sorry, no late assig
MAT 1332. Winter 2016, Assignment 6
Due Monday April 11 in the math department dropboxes by 7:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math depart
MAT 1322,
MIDTERM 1,
VERSION A
1. [2 points, 7.2 #19] Use Eulers method with step size 0.2 to estimate y(0.4), where y is the solution of the initial value problem y= 2x+y , y(0) =1. A. 1.2 B. 1.46 C.
MAT 1322B,
Winter 2005
Professor: Venanzio Capretta
MIDTERM TEST 3, version A Solutions
1. [2 points, 8.6 #8] Find a power series representation of the function: f (x) =
3 n 2n n=0 ( 2 ) x n=0
3x 1 2
MAT 1322E,
Winter 2005
MIDTERM TEST 2Solutions
Family NAME: Given NAME: Student Number: MAX=18 Time: 80 min. (Includes time for distribution of papers.) Only TI 30-type calculators are permitted. Note
MAT 1322, Winter 2005
SOLUTIONS TO TEST 1 (Version 1)
1. [2 points, 5.10 #17] Determine if the integral is convergent. A. 0.25 B. 0.11 C. 0.125 D. 0.333 Solution. By parts: u = x, v = e , u = 1, v = 1
MAT 1322 MIDTERM 1, VERSION A
1 1. [2 points, 5.10 #19] Determine if the integral 2 x(ln x)2 dx is convergent or divergent and evaluate if it is convergent. A.1 B.2.51 C.0.50 D.5.33 E.1.44 F.divergent
MAT 1322, Winter 2005 SAMPLE EXAMINATION MAX = 46 points
This sample exam is last years nal exam slightly modied to t this yearss format. The correct answers of multiple choice problems are indicated
MAT 1322 Winter 2004
MIDTERM TEST 3 Version A
1. [2 points, 8.8 #7] Find the MacLaurin series c0 + c1 x + c2 x2 + c3 x3 + of 1 the function 9+6x . The coecient c3 and the radius of convergence R is A.
Mat 1322D, Calculus 2 Professor. Arian Novruzi Department of Mathematics email: [email protected] tel: (613) 562 5800 x 3530 Lastname, Firstname: Student number:
November 3rd, 2004
MIDTERM 2 (time 80
University of Ottawa MAT 1332B Midterm Exam
March 31, 2008. Duration: 80 minutes. Instructor: Frithjof Lutscher
Family Name:
First Name:
Do not write you student ID number on this front page. Please w
MAT 1332, Winter 2015, Assignment 1
Due Thursday January 29 by 9:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math department will not lend you a stap
April 19, 2012 Midterm MAT1332D
Winter 2012
Study guide - Final Exam
As you read these let me know if you think I have missed anything. I will add more as I
can.
The best way to study is:
1. make sure
Professor Jason Levy, University of Ottawa, MAT 13320, Winter 2011
Assignment 3 Solutions
1. For each of the following improper integrals, determine whether it converges, and
evaluate it if if does.
(
MAT1332, Winter 2011, Assignment 1 Solutions
Total=7 points.
1. (1 point) (a) Use the substitution u = 3 1415. Then élt = 14, so dt = :114. Thus
/314tdt_ Ed_lnlul+0lnl314tl+0
(Dont forget to resubst
MAT 1332, Winter 2017, Assignment 4
Due Wednesday March 8 in the math department dropboxes by 7:00pm.
Late assignments will not be accepted; nor will unstapled assignments.
Professors in the math depa
MAT 1332, Winter 2009, Assignment #3, Solutions
Total marks=29. [2] 1. Using the substitution u = 2+5x, then du = 5dx, and then we find that dx = are from u = 2 to u = . Therefore,
0 du 5 ,
and the l
MAT 1332, Winter 2007, Assignment #2, Solutions
Total marks=11. [2] 1. If you simply integrate, the answer is zero. So that obviously isn't right. It's best to sketch the two graphs. See Figure 1.
1 A
Tutorial #10 - MAT 1332A - Fall 2009 November 23, 2009
Find the eigenvalues and eigenvectors of A = Solution: 1 = 2 + 2i, v1 = 1 2 + 2i
0 8
1 4
. 1 2 2i
; 2 = 2 2i, v2 =
On any given day, a student
Tutorial #9 - MAT 1332A - Fall 2009 November 16, 2009
4 Let A = 2 0
0 5 0
2 4 . Find the eigenvalues and eigenvectors of A. 5
= Answer: 1 5 is an eigenvalue whose corresponding eigenvectors are 2 0 v
Tutorial #8 - MAT 1332A - Fall 2009 November 9, 2009
Section 5.1: questions 17 and 21 30 4 1 Let A = 1 2 , B = 0 2 11 following (where possible): (a) 2AT + C (b) AB (c) CB (d) tr(CC T ) (e) det A (f)
Solutions to Assignment 2 - MAT1332A - Fall 2009 (1) (a) [6 points] Check that N (t) = equation t is a solution of the dierential 1 + ct
dN N2 = 2 . Treat c as an unspecied constant. dt t
(b) [5 point
Solutions to Assignment 1 - MAT1332A - Fall 2009
(1) Evaluate
/2
3 cos 2 d.
Solution: First, lets make a change of variable. Let u = 2 . So du = 2d. Then
1 cos d = 2
3 2 /2 /2
u cos u du.
Now we
Systems of dierential equations (the complex case) and double integrals over rectangles 1. Find the general solution of the system: (a) x1 = 2x1 5x2 x2 = 4x1 2x2 x1 = x1 2x2 x2 = 2x1 + x2 x1 = 5x1 9x2
The chain rule (general version) Find z/u and z/v by using the chain rule. (a) z = xey + yex , x = u sin v , y = v cos u (b) z = xey , x = ln u, y = v (c) z = xey , x = u2 + v 2 , y = u2 v 2 (d) z = s
Critical points and their classication, chain rule (the simplest version) 1. Find all critical points and classify them as local max, local min, or saddle point. (a) f (x, y ) = 2x2 + y 2 + 4x 4y + 5
Gradient and directional derivative 1. Find the grad f and the grad f (P ). (a) f (x, y ) = 3x 7y , P (17, 39) (b) f (x, y ) = 3x2 5y 2 , P (2, 3) (c) f (x, y ) = ex
2
y 2
, P (0, 0)
2. Find the dire