Problem Set 12 - Due by Thursday, March 22, 2012
Posted/Revised: March 14, 2012
Note: SHE = Calculus (tenth edition) by Salas, Hille, and Etgen
Problems marked with * are to be handed in during lecture or in SS1071.
Please write your three character tutor
MAT 137Y: Calculus!
Problem Set 4.
Due in tutorial on November 10-11
Instructions:
You need to turn in this assignment in the tutorial in which you are
enrolled.
Before you attempt this problem set, do all the practice problems from
sections 3.7, 4.10,
MAT 137Y: Calculus!
Problem Set 3.
Due in tutorial on November 3-4
Instructions:
You need to turn in this assignment in the tutorial in which you are enrolled.
Before you attempt this problem set, do all the practice problems from sections
3.13.6 (see c
MAT 137
Tutorial #6 Related rates
November 3-4, 2013
1. We are inating a spherical balloon. At what rate is the volume of the balloon
changing when the radius is increasing at 3cm/s and the volume is 100cm3 ?
2. A highway patrol ocers radar unit is parked
MAT 137
Tutorial #8 Applied optimization problems
November 2425, 2013
1. You have the opportunity to enter a new business manufacturing luxury Anacleto
boxes. An Anacleto box is a square open box: the bottom is a square, the four sides
are equal rectangle
MAT 137
Tutorial #7 Inverse trigonometric functions
November 1011, 2013
Recall that the following two functions
y = sin x,
x = arcsin y,
x
2
2
1y1
are inverses of each other. This implies:
1 u 1,
arcsin(sin u) = u
for all
u .
2
2
If you get confused, it m
MAT 137
Tutorial #5 Computation of derivatives
October 27-28, 2013
1. Compute the derivative of the following functions:
(a) f (x) =
p
x
(b) f (x) = 3x2 + 5x + 1
(c) f (x) =
x7
3x3
6x4
Hint: there is a shortcut.
(d) f (x) =
p
x(x2 + 2)
Hint: there is a sh
import tictactoe_functions
import builtins
# Get the initial value of the constant
constant_before = [tictactoe_functions.EMPTY]
# Type check and simple test for tictactoe_functions.is_between
result = tictactoe_functions.is_between(2, 1, 3)
assert isinst
MAT 137Y: Calculus!
Problem Set 1.
Due in tutorial on May 18/19
Instructions:
Print this cover page, fill it out entirely, sign at the bottom,
and STAPLE it to the front of your problem set (You do not need
to print out the questions.) Doing this correctl
MAT 137Y: Calculus!
Problem Set 2.
Due in tutorial on May 25/26
Instructions:
Print this cover page, fill it out entirely, sign at the
bottom, and STAPLE it to the front of your problem
set (You do not need to print out the questions.) Doing this correctl
MAT 137
Tutorial #1 Logic
May 16 - 17, 2016
1. Write the negation of each of the following statements in as simple a way as possible.
(a) My favourite prime number is greater than 2.
(b) For every problem there is a solution.
(c) There is a building more
MAT 137Y: Calculus!
Problem Set 5.
Due in tutorial on July 6/7
Instructions:
Print this cover page, fill it out entirely, sign at the bottom,
and STAPLE it to the front of your problem set (You do not need
to print out the questions.) Doing this correctly
MAT 137Y: Calculus!
Problem Set 7.
Due in tutorial on July 27/28
Instructions:
Print this cover page, fill it out entirely, sign at the bottom, and STAPLE it to the front of your problem set (You do
not need to print out the questions.) Doing this correct
MAT 137Y: Calculus!
Problem Set 4.
Due in tutorial on June 15/16
Instructions:
Print this cover page, fill it out entirely, sign at the bottom, and STAPLE it to the front of your problem set (You do
not need to print out the questions.) Doing this correct
MAT 137Y: Calculus!
Problem Set A.
This problem set is intended to help you prepare for Test #1. It is not comprehensive: it only contains some problems that were not included in past problem sets
or in past tutorials. You do not need to turn in any of th
MAT 137Y: Calculus!
Problem Set 6.
Due in tutorial on July 13/14
Instructions:
Print this cover page, fill it out entirely, sign at the bottom, and STAPLE it to the front of your problem set (You do
not need to print out the questions.) Doing this correct
MAT 137Y: Calculus!
Problem Set 5.
Due in tutorial on November 24-25
Instructions:
You need to turn in this assignment in the tutorial in which you are
enrolled.
Before you attempt this problem set, do all the practice problems from
sections 7.1, 7.7, t
Lecture 4
1
Continuity
Recall from last lecture the definition of limits.
Definition. Let f be a function defined at least on an open interval (cp, c+p)
except possibly at c itself. We say that lim f (x) = L if for every > 0 there
xc
exists > 0 such that
1
If. . . , then. . . statements
In general, a mathematical statement is an implication i.e. it consists of a hypothesis followed
by a conclusion.
Implications, also called conditional statements, are very often written as an if P , then
Q statement where
MAT137Y, 2010-2011 Winter Session, Solutions to Term Test 3
1. Evaluate the following integrals.
e
ln(x)
(a) (7%)
dx
x3
1
Here we use integration by parts:
1
dv = x3 dx
1
v = 2x2 .
u = ln(x)
1
du = x dx
e
1
(b) (9%)
e
ln(x)
1
1
dx = 2 ln(x) +
3
x
2x
2
1
1
Department of Mathematics, University of Toronto
Term Test 3 - March 16, 2011
MAT137Y, Calculus!
Time Alloted: 1 hour 50 minutes
1. Evaluate the following integrals.
e
ln(x)
(a) (7%)
dx
x3
1
1
(b) (9%)
dx
(1 x2 )5/2
x2
dx
(x 1)2 (x + 1)
(c) (8%)
2.
x
1
(a
MAT137Y 20092010 Winter Session, Solutions to Term Test 3
1. Evaluate the following integrals.
(8%) (i)
dx
.
x(ln x)5/2
Let u = ln x. Then du = 1 dx, thereby giving us
x
du
=
u5/2
2
2
u5/2 du = u3/2 + C = (ln x)3/2 + C.
3
3
1
(8%) (ii)
arctan x dx.
0
We i
Department of Mathematics, University of Toronto
Term Test 3 - March 2010
MAT137Y, Calculus!
Time Alloted: 1 hour 50 minutes
1.Evaluate the following integrals.
dx
(i) (8%)
x(ln x)5/2
1
(ii) (8%) Find
arctan(x)dx
0
(iii) (10%)
dx
(2 + x2 )2
(iv) (10%)
1 x
Department of Mathematics, University of Toronto
Term Test 1 November 15, 2006
MAT 137Y, Calculus!
Time Alloted: 1 hour 50 minutes
1. Evaluate the following limits. Do not use LH pitals Rule to evaluate the limit.
o
(x 1)2 1
.
x0
x2 + 6x
sin2 (5t )
(7%) (