MATH 1009E
TEST 1: Solutions
September 2015
PART A: MULTIPLE CHOICE QUESTIONS.
A1.
The domain of the function f (x) =
9 x is
(a) [3, 3], or, equivalently, cfw_3 x 3.
(b) (9, ), or, equivalently, cfw_x > 9.
(c) [9, ), or, equivalently, cfw_x 9.
(d) (, 9],
MATH 1009 Test 1
MATH 1009  B
January 2012
Page 1
TEST 1
LAST then FIRST name (please PRINT clearly).
STUDENT NUMBER: .
This test is worth 40 marks. The test paper cannot be taken from the examination room.
Nonprogrammable calculators are required.
PART
MATH 1009E
TEST 2  Solutions
October 2015
PART A: MULTIPLE CHOICE QUESTIONS.
[5 3 marks each = 10 marks]
A1.
(a)
A2.
lim
x0
3x5 2x3 + 7x + 1
x5 + 5
1
5
lim
x3
lim
x
x
(a) 3
A5.
(e) None of the above.
(c) 0
(d)
(e) None of the above.
7x4 + x3 + 32 x 3
i
MATH 1009E
TEST 2
October 2014
LAST then FIRST name (please PRINT clearly).
STUDENT NUMBER: .
This test is worth 40 marks. There are 3 pages (please count!) Nonprogrammable calculators
are required.
PART A: MULTIPLE CHOICE QUESTIONS.
[5 2 marks each = 1
MATH 1009E
TEST 2  solutions
October 2014
PART A: MULTIPLE CHOICE ANSWERS: a, b, b, d, d.
[5 2 marks each = 10 marks]
A1.
(a)
A2.
lim
x0
3x5 2x3 + 7x + 1
x5 + 5
1
5
lim
x3
lim
x
(e) None of the above.
(c) 3
(d)
(e) None of the above.
3x5 + x3 4x2 11
is
MATH 1009*B
TEST 3
March 2013
LAST then FIRST name (please PRINT clearly).
STUDENT NUMBER: .
Section:
B1
B2
B3
This test is worth 40 marks. The test paper cannot be taken from the examination room.
Nonprogrammable calculators are allowed.
1. [8 Marks]
de
MATH 1009
TEST 3  SOLUTIONS
March 2013
Based on sections 3.2.4 (Implicit dierentiation), 4.1  4.5(up to the Absolute Extremum).
1. [8 Marks]
decreasing:
Find the intervals where each function f is increasing and those where it is
[3] (a) f (x) = e3x .
[
MATH 1009
TEST 1 Solutions
PART A: MULTIPLE CHOICE QUESTIONS. 2 marks are given for the correct
answer, 0  otherwise. b, a, c, d, a, a, d.
2 marks are given for the correct answer, 0  otherwise. ( b, a, c, d, a, a, d.)
A1.
The domain of the function f (
MATH 1009  E
TEST 3  SOLUTIONS
October 2015
1. [17 marks]. Find the derivative of the following functions using the appropriate rules of
dierentiation:
[3] (a) f (x) = (x5 + 3x3 + 1)(7x2 x 23). (Do not simplify the result.)
2x2
. (Simplify the numerator
PART AMULTIPLE CHOICE. DO ALL QUESTIONS. 2 MARKS EACH Answer on attached sheet. Be sure to detach and hand in with your exam. Figure1
1. Refer to Figure 1. What is the opportunity cost to society of bananas when considering the movement from point A to po
Carleton University
School of Mathematics and Statistics
Math 1009 Calculus Practice Test #3 of 4
NAME: _
STUDENT NUMBER: _
INSTRUCTIONS: There are TWO written questions. Each question outlines its own marking scheme. Please read each question carefully.
MATH1009E
Calculus: with applications to Business and Economics
Instructor:
Fall 2013
Mathieu Lemire
Oce: 5250 Herzberg Building
Tel.: 6135202600 ext. 1983
Email: mathieu.lemire@carleton.ca or through cuLearn.
Lectures: Mondays and Wednesdays from 13:0
Page
1
Note: This tutorial is too long to be worked through in one session. Please do as many
problems in class as you can, and then the rest are for the students to finish at home. In order
to prepare for Test 1, it is important to work through all the p
MATH 1009A
TEST 2  solutions
February 2016
PART A: MULTIPLE CHOICE ANSWERS: b, a, d, b, c .
[2 marks each =10 marks]
A1.
(a)
lim
x0
2x4 x3 + 9x + 6
5x4 + 2
2
5
A2.
x2
lim
x
(d)
(e) None of the above.
7x5 + 3x3 9x2 + 1
is
x2 + x + 17
(b) 0
lim
x
(a) 4
A
Page
1
=
TUTORIAL
Chapter 2 LIMITS
Example 1.
Find lim
x2
3x2 + x 7
.
x3 + 2
3x2 + x 7
is a rational function, and since its denominator is not zero at x = 2, the
x3 + 2
function is continuous at x = 2. Therefore, the limit may be computed by evaluating t
CARLETON UNIVERSITY
FINAL/DEFERRED
EXAMINATION
November 2012
DURATION:
3
HOURS
Department Name & Course Number:
Mathematics and Statistics MATH 1009*EF
Course Instructor(s) : Dr E. Devdariani, Dr R. Cova.
AUTHORIZED MEMORANDA
Non programmable, non graphin
MATH 1009 *C
TEST 1 Solutions
PART A: MULTIPLE CHOICE QUESTIONS.
2 marks are given for the correct answer, 0  otherwise. ( d, a, d, b, b, c, a.)
A1.
The domain of the function f (x) =
1
4x
is
(a) [2, 2], or, equivalently, cfw_2 x 2.
(b) (4, ), or, equiv
MATH 1009C
TEST 2  solutions
February 2014
PART A: MULTIPLE CHOICE ANSWERS: b, a, d, b, c .
[2 marks each =10 marks]
A1.
(a)
lim
x0
2x4 x3 + 9x + 6
5x4 + 2
2
5
A2.
x3
lim
x
(d)
(e) None of the above.
7x5 + 3x3 9x2 + 1
is
x2 + x + 17
(b) 0
lim
x
(a) 4
A
Chapter 6.1_Q9: Determine the integral, and verify your answer by differentiating:
+2
Problem Solving  What are the terms/strategies I may need? What do I know?
Basic Techniques of Integration:
Asking what function would derive to make _ , then multipl
MATH 1009B
TEST 1: Solutions January 2016
PART A: MULTIPLE CHOICE QUESTIONS.
A1.
The domain of the function f (x) =
4 x is
(a) (4, ), or, equivalently, cfw_x > 4.
(b) [4, ), or, equivalently, cfw_x 4.
(c) (, 4], or, equivalently, cfw_x 4.
(d) x R.
(e) no
MATH 1009 B
TEST 3  SOLUTIONS
March 2016
1. [8 Marks]
decreasing:
Find the intervals where each function f is increasing and those where it is
[3] (a) f (x) = e3x .
[5] (b) f (x) = x3 27x.
Solution:
(a) f 0 (x) = e3x (3 x)0 = e3x < 0 for all real x. Thus
MATH 1009  B
TEST 4
March 2016
SOLUTIONS

1. [12 Marks] Find fx , fy , fxx and fyy of the following functions:
[4] (a) f (x, y) = 2x3 y 5 + xy 3 .
[4] (b) f (x, y) = e2xy .
[4] (c) f (x, y) =
3x
.
y
Solution:
(a) fx = 6x2 + y 3 ;
fy = 5y 4 + 3xy 2 ;
(b)
Page
1
Chapter 4 APPLICATIONS OF THE DERIVATIVE
Example 1. (Minimizing the surface area of a box) A box with a square base and
open top must have a volume of 4, 000 cm3 . Find the dimensions of the box that minimize the
amount of the material used.
Soluti
Solutions to the final examination review for MATH 1009
PART A. MULTIPLE CHOICE QUESTIONS. Each answer is worth 3.5 marks.
Answers: dcada bcbdb adacb daabc
3x5 x + 5
.
x 1 3x2 + x4
1. Evaluate lim
(a) 3.
(b) 1.
(d) .
(c) 0.
(e) None of these.
Answer: (d)
Introduction to the Study of Psychology PSYC1001  Section F NOTE: THESE NOTES FOR TODAY ARE THE BEGINNING OF THE MATERIAL FOR MIDTERM #2 In todays class 0. The Nervous System 0. The Central Nervous System 0. The Brain 1. The Brain & Behaviour 1. The Peri
Introduction to the Study of Psychology  PSYC1001  Section F In todays class Chapter 3 0. Genetics: how much of human behaviour is biologically (genetically) predetermined? 1. How do genes determine who we are? 2. Evolution: how does our evolutionary hi
Introduction to the Study of Psychology  PSYC1001  Section F In todays class 0. Chapter 5 0. How do we detect and process information from our environment? 1. How are environmental stimuli received and turned into neural patterns? 1. 2. 3. 4. From the t
Introduction to the Study of Psychology
PSYC1001  Section F
In todays class
Chapter 5
How do we detect and process information from our environment? How are environmental stimuli received and turned into neural patterns?
From the text
What are Sensatio
Introduction to the Study of Psychology
PSYC1001  Section F
In todays class
Chapter 3 Genetics: how much of human behaviour is biologically (genetically) predetermined? How do genes determine who we are? Evolution: how does our evolutionary history infl
MATH 1009 TUTORIAL CHAPTER 1: ELEMENTARY FUNCTIONS
1.1 Definition, Domain and Range of a Function
(1) Find the domain of the following functions.
p
(c) h(x) = p x2 + 1
(d) p(x) = (x 1)(x
(a) f (x) = (x + 3)2
x
(b) g(x) = 2
(x
4)(x + 1)
3)
(e) k(x) = p
5
(