Mathematics 137
October 29, 2014
Assignment 3 (due Wednesday, November 5 at the beginning of your tutorial)
Problem 1. Find f (c) if it exists.
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f (x) =
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2x3 + 1, x > 1
and c = 1
Problem 2. Give an example of a function f such that f (x) exi
MAT137Y5Y
Solutions to Assignment 2
September 30, 2015
1. (a) The domain of f is [0, 3) and its range is [0, 2].
(b) The slope of the first line segment is m =
the equation y = 2x.
20
10
= 2 and its yintercept is 0. It is thus described by
12
= 12 . The
MAT137Y5Y
Practice Term Test I
Fall 2015
Name:
Student number:
Tutorial (circle one):
Wed 5pm  7pm
Wed 11am  1pm
Thu 3pm  5pm
Wed 1pm  3pm
Thu 5pm  7pm
There are 6 questions on this practice term test. On the actual term test, be sure to
explain your
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Mathematics 137
February 18, 2015
Assignment 5 (due Wednesday, February 25 at the beginning of your tutorial)
Problem 1. Calculate
(a)
x sec2 (x2 )dx
(b)
1
cos2
0
(c)
1
1
( )
x dx
2
7x5 3 x dx
Problem 2. Calculate the area of the region in the rst quadran
Mathematics 137
October 8, 2014
Assignment 2 (due Wednesday, October 15 at the beginning of your tutorial)
Problem 1. Give , proof for the following statements
(a) limxc x = c for any c > 0,
(b) limx2 x 2 = 0.
Problem 2. Evaluate the limits that exist.
Mathematics 137
January 14, 2015
Assignment 4 (due Wednesday, January 21 at the beginning of your tutorial)
Problem 1. Give an example of a continuous function (not piecewise) with two
dierent horizontal asymptotes. Justify your answer. (Note that your ex
Mathematics 137
September 17, 2014
Assignment 1 (due Wednesday, September 24 at the beginning of your tutorial)
Problem 1. Let p be prime. Show that
p is irrational.
Problem 2. Given that 0 a b. Show that
a+b
b
a ab
2
Problem 3. For any natural n dene s(
MAT137Y5Y
FALL 2015
SOLUTIONS TO HOMEWORK 1
(1) Dividing the inequality by 3 yields
8
5
x2 x .
3
3
Then, we add
25
36
to both sides to complete the square. This yields
2
5
121
x
.
6
36
Taking square root of both sides yields
x 5 11 .
6
6
Thus, we have eit