MAT 1322 A
Assignment 1 (Due Wed. Jan. 21st at 8:30)
Student Number:
For Problems 1 4, determine if the improper integral converges or diverges. If the integral converges,
give its value.
1.
1
ln x
dx
x2
Answer:
Solution:
6
2.
0
x
dx
(x 4)3
Solution:
Answ
MAT 1322
SAMPLE EXAMINATION
Time: 3 hours
Calculators are permitted. (Non-programmable, non-graphing, no dierentiation or integration capability.) Notes or books are not permitted.
Work the problems in the space provided. Use the back-pages for rough work
Calculus II
MAT1322 A
Test 2
Professor: Benoit Dionne
True or False
Question 1 (4 points)
For each of the following statements, determine if it is true or false (circle your answer).
an converges, then lim an = 0.
If the series
TRUE
FALSE
TRUE
FALSE
TRUE
Calculus II
MAT1322 A
Test 1
Professor: Benoit Dionne
Multiple Choice Questions
2 points
Question 1
Find the volume of the solid whose base is the region of the plane enclosed by the curves
y = 3x, y = x2 and x = 2; and the cross sections perpendicular to
MAT 1322 B
W2007
Monday, Feb. 12th 10:0011:20
Prof. Dr. Hua
MIDTERM TEST 1
Max = 20
Student Number:
Time: 80 min.
Only Faculty of Science approved calculators (TI30xx) are permitted. Notes or books
are not permitted.
Work all problems in the space provi
MAT 1322 E, Winter 2005
Professor: Hua
FINAL EXAMINATION
NAME:
Student Number:
MAX = 46 points
Time: 3 hours
Only TI 30-type calculators are permitted. Notes or books are not permitted.
Problems 1-4 [4 points each] require detailed and clearly presented s
MAT 1322 B
Assignment 3 (Due Wed. Feb. 27th at 8:30)
Student Number:
1. (i) Find the Taylor Polynomials P1 (x) and P2 (x) for the function f (x) = 1/x near the point
x = 2.
Solution:
Answer: P1 (x) =
P2 (x) =
(ii) Carefully draw the graphs of f (x), P1 (x
MAT 1322 B
Assignment 2 (Due Wed. Jan. 30th at 8:30)
Student Number:
1. Find the volume of the solid obtained when the region bounded by the curves y = x and y = x is
rotated around the line y = 2 .
Solution: Volume =
2. Find the volume of the solid whose
MAT 1322 B
Assignment 5 (Due Wed. March 12th at 8:30)
Student Number:
1. A thermometer is taken from a room at temperature 22 C and placed outside, where the temperature is
5 C. One minute later, the thermometer reads 7 C. Using Newtons Law of Cooling, nd
MAT 1322 B
Assignment 4 (Due Wed. March 5th at 8:30)
Student Number:
1. For what values of does y = cos(t) satisfy y + 5y = 0 ?
Solution:
Answer: =
2. Consider the initial value problem y = 2xy, y(0) = 1 .
(a) Use Eulers Method to estimate y(1), with (i)
MAT 1322 B
Assignment 1 (Due Wed. Jan. 16th at 8:30)
Student Number:
For Problems 1 4, determine if the improper integral converges or diverges. If the integral converges,
give its value.
1.
0
x
dx
ex
3
2.
0
dx
9 x2
Solution:
Solution:
10
3.
1
4.
e
2 dx
(
MAT1322-Review
7.7 Improper Integrals
Type I (Innite Interval)
t
f (x)dx = lim
t
a
f (x)dx =
b
a
f (x)dx = lim
c
f (x)dx +
b
f (x)dx,
c
t
f (x)dx,
t
f (x)dx.
Type 2 (Discontinuous Integrand)
If f (x) is continuous on [a, b), then
b
t
f (x)dx = lim
tb
a
Calculus II
MAT1322 A
Test 2
Professor: Benoit Dionne
True or False
Question 1 (4 points)
For each of the following statements, determine if it is true or false (circle your answer).
Suppose that 0 an bn and that
n
bn converges, then
an
TRUE
FALSE
TRUE
FA
Calculus II
MAT1322 A
Test 1
Professor: Benoit Dionne
Multiple Choice Questions
2 points
Question 1
Find the volume of the solider whose base is the region of the plane enclosed by the curves
y = x/2, y = x2 and x = 3; and the cross sections perpendicular
MAT1332: Calculus for the Life Sciences II - Part 1
Dr. Robert Smith?
1
Review of integrals
1.1
Power rule
Eg)
Z
xn dx =
Z
Eg)
1.2
Z
y
Z
Logarithms:
Z
Trigonometric functions:
Z
Z
Hint:
t3 dt =
3
dy =
t4
+c
4
y
2
2
+c
Special Functions
Exponentials:
Eg)
x
7
Functions of Several Variables
Suppose you run a company which produces two types of television. Let x1 be the quantity
of type 1 and x2 be the quantity of type 2. Then the usual functions in which we are
interested (prot, revenue, and cost) will depend
1
MAT1322 Calculus II
Assignment #1
Question 1
4
4 points
1
dx as the limits of denite integrals. Dont compute the integrals.
x(x 2)
Express
0
Solution:
We have an improper integral because x(x 2) = 0 at x = 0 and x = 2; both points in the
interval [0, 4]
m t; um L <( um Zak as, aw
waK
C) l( (4W Kh*(;L>\ 9M Ea koUo.
Ipvf/(
(a; [6 km :\ La 66 Jawué 9A7
so H R
n " 0
EV Z 7' a» 7/ s
_. w
"" M
GLer (VH4) Awe! (Pct Z
K 2 LW" 7 MM:
4, M 44 Mar) I 1
Mann "' W M /.2
H l ( ¢ CVLJ5'6(»/LZ/Qj (p
Calculus II
MAT1322 A
Test 1
Professor: Benoit Dionne
Multiple Choice Questions
2 points
Question 1
Find the volume of the slide whose base is the region of the plane enclosed by the curves
y = 2x, y = x2 and x = 3; and the cross sections perpendicular to
Calculus II
MAT1322 A
Test 2
Professor: Benoit Dionne
True or False
Question 1 (4 points)
For each of the following statements, determine if it is true or false (circle your answer).
an converges, then the series
If the series
an converges ab-
TRUE
FALSE