Tuesday, September 12, 2017
MAT137
A mathematical definition clearly and unambiguously defines a mathematical concept.
o For example, a function, f, is periodic if there exists a positive real number,
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
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
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,
arcs
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
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
MAT 137
Tutorial #9 LHpitals Rule
o
January 56, 2014
1. Compute the following limits:
p
x+1
x
tan(3t)
(a) lim
t!0 ln(1 + 2t)
(f) lim
h3
(b) lim 3
h!2 h
(g) lim x tan
x!0
5h2 + 3h + 6
h2 3h + 2
x!1
1 c
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, d
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,
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,
Given name:_
Family name:
Student n u m b e r : _
Signature:
Tutorial (circle one):
LM157-Natasha
WE76-Malle
SS621-Jason
IN209-Thivviya
LM123-N0ra
U N I V E R S I T Y OF T O R O N T O
Faculty of Arts
DURATION: 3 hours
December 2015
University of Toronto
Faculty of Arts & Science
FINAL E X A M I N A T I O N
MAT223H1F
Linear Algebra I
E X A M I N E R S : T . Bazett, I. Biborski, N. Garcia-Fritz, S.
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 no
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 no
Tuesday, September 19, 2017
MAT137
Let f:R -> R, and C and L be real numbers.
o The limit is x approaches C of f is L, written lim x->c f(x) = L.
o If x gets arbitrarily close to C, f(x) gets arbitrar
Thursday, September 14, 2017
MAT137
When you are given two sets, S and T, a function assigns every value in S to a value in T.
(f:
S -> T)
The domain must come with the function in the beginning.
o Ch
Tuesday, September 19, 2017
MAT137
The absolute value of a number that is equal to or above 0 is the number itself.
o The absolute value of a negative number is the number, but without the negative si
MAT 137Y: Calculus!
Problem Set B.
This problem set is intended to help you prepare for Test #2. It is not comprehensive: it only contains some problems that were not included in past problem sets
or
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
n
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
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
n
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
n
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
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 pro
April 18, 2016
DURATION: 3 hours
University of Toronto
Faculty of Arts & Science
AUL-
FINAL EXAMINATION
MAT223H1S
Linear Algebra I
EXAMINERS: T. Bazett, N. Garcia Fritz, L. Garcia Martinez, Y. Qing, X
DURATION: 3 hours
June 20, 2016
University of Toronto
Faculty of Arts 81 Science
FINAL EXAMINATION
MAT223H1S
Linear Algebra I
EXAMINERS: T. Bazett, J. Lane, Y. Qing
Last Name ( P R I N T ) :
Given Nam
ww
w.
ox
di
a
MAT137Y1 - Calculus!
Test 3 Solutions
February 5th, 2014
.c
om
1.
(a) Calculate
4
X
1
i=1
i
.
i=1
(b) Calculate
Z
Z
1 1 ow1nl 1 25
o
= + + +
=
i
1 2 3 ad4er 12
ID
sin x dx.
21
14
0
/3
x=
gegmiﬁ
Cm¥n'amgjl,
\n meg dub Lgnawae, we 3&3 59nd? Son-Ghma '6‘ TE EX goes miXA/LoA ink-Wm
omci mkWuJ-‘r ohxug’c charges.
\m manaXics) .Une wow Mmous has a we“ S\01\Q( meaning.
high'ﬁchcﬂ 43mg“ 0~ Ma
ww
w.
ox
di
a
.c
om
MAT137Y1 - Calculus!
Test 3. February 7th, 2015
Time: 105 minutes
Please, fill this page with ALL CAPITAL LETTERS:
Last name . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Final Examination April 2016
MAT137Y1
University of Toronto
Faculty of Arts and Sciences
Final Examinations - April 2016
MAT137Y1 - Calculus!
Time: 3 hours
Instructors: T. Bazett, P. Crooks, A. Gracia
Faculty of Arts and Science
Department of Mathematics
University of Toronto
MATH 135H1S - Calculus 1(A)
Final Examination
Duration: 3 hours
April 2016
Aids allowed: None
Fill in the information on thi
MAT137Y1
Final Examination August 2016
UNIVERSITY OF TORONTO
Faculty of Arts and Science
AUGUST 2016 EXAMINATIONS
MAT137Y1 - Calculus!
Duration - 3 hours
N O AIDS ALLOWED
Instructors: R. Lareau-Dussau
DURATION: 3 hours
Thursday June 23, 2016
University of Toronto
Department of Mathematics
FINAL EXAMINATION
MAT135H1F
Calculus I
EXAMINERS: T. Balehowsky, K. Luk
Last Name (PRINT):
Given Name(s) (PRINT