Fall Term, 2013
Name: 5 c9 lull-(19h 3
Tutorial Time:
Class Section: A8z30AM B12z30PM
WILFRID LAURIER UNIVERSITY
Waterloo, Ontario
Mathematics 103 Calculus I
Midterm October 30, 2013, 5:30PM
Instructor:
Dr. Chester Weatherby
Time Allowed: 80 minutes
Tot
MA121 Mock Final Exam
Name:
Time Allowed: 150 minutes
Total Value: 100 marks
Number of Pages: 8
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while completing the mock test. Please note, that the cheat
MA103 Mock Midterm
Name:
Time Allowed: 80 minutes
Total Value: 60 marks
Number of Pages: 6
Instructions:
Non-programmable, non-graphing calculators are permitted. No other aids allowed.
Check that your test paper has no missing, blank, or illegible pages.
MA103 Midterm Test
[10 marks]
2013 Fall
Page 1 of 2
1. Without using LHpitals Rule, evaluate the following limits if they exist:
o
x2 x2
x2 x2
(a) lim
2x10
|x5|
lim x+255
x
x0
4x4 +3
lim x2 3x3/2 +2
x
(b) lim
x5
(c)
(d)
eAx
when x < 0,
For what values of
2012 Fall
MA103 Midterm Test
[4 marks]
Page 1 of 2
1. Find a formula for the inverse of the function
f (x) = 1 + 3 2x,
x 3/2.
Also, determine the domain of the inverse function.
[3 marks]
[3 marks]
2. (a) State the Intermediate Value Theorem.
(b) Show tha
MA170 Mock Final Exam
Name:
Time Allowed: 150 minutes
Total Value: 100 marks
Number of Pages: 9
Instructions:
Cheat Sheet:
One 8:5" 11" page of study notes (both sides) is allowed as a reference
while completing the mock test. Please note, that the cheat
MA103 Mock Final Exam
Name:
Time Allowed: 120 minutes
Total Value: 100 marks
Number of Pages: 9
Instructions:
Non-programmable, non-graphing calculators are permitted. No other aids allowed.
Check that your test paper has no missing, blank, or illegible p
MA103 Mock Midterm
Name:
Time Allowed: 80 minutes
Total Value: 60 marks
Number of Pages: 6
Instructions:
Non-programmable, non-graphing calculators are permitted. No other aids allowed.
Check that your test paper has no missing, blank, or illegible pages.
MA103, Winter 2012 - Final Examination
[4 marks]
Page 1 of 12
1. Find the following limits:
x2 + 1 x
(a) lim
x
2
x
[4 marks]
(b) lim x2 sin
[4 marks]
(c) lim (2 + x)1/x (Hint: LHospitals rule)
x0
(Hint: Squeeze theorem)
x
Over
MA103, Winter 2012 - Final E
MA103 - Final Examination
Page 1 of 1
Antiderivatives
Trigonometric Identities
Z
f (u) du denotes the
general antiderivative of f (u).
Z
If
Z
f (u) du = F (u) + c then
dF (u)
= f (u).
du
un+1
u du =
+ c, n 6= 1
n+1
Z
1
du = ln |u| + c
Z u
eu du = eu + c
Z
MA103 Mock Exam
Answers
(Full Solutions will NOT be posted;
use the MACs drop-in help centre if you have any questions.)
* Please remember that the mock test was meant as a means of providing an extra set of practice
questions and basis for a review class
MA103 Mock Final Exam
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the midterm based solely on the topics covered by the mock
test! Go back thro
MA103 Midterm, Fall Term 2009
Page 1
Disclaimer: Tests and exams from previous o erings of mathematics courses are posted to the on-line Exam
Bank, administered by the Mathematics Assistance Centre, as a courtesy to WLU students. Past exams
should be used
Chapter 4 Trigonometry
Chapter 4 Prerequisite Skills
Chapter 4 Prerequisite Skills
Question 1 Page 200
a)
5
cos =
3
4
3
, tan =
5
4
4
b)
Using the CAST rule; sine and tangent are negative:
sin =
12
12
, tan =
5 5
13
12
13
c)
Using the CAST rule; cosine
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, [email protected]
Lecture 18. Extreme values and relative extremals (4.1)
Note: I am not covering all possible types of examples because its just physically impossible due to time constraints. You can get better r
Calculus I
Winter term, 2016
Lecture 21. Curve sketching and second order derivative (4.5)
Note: I am not covering all possible types of examples because its just physically impossible due to time constraints. You can get better results when you read
the
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, [email protected]
Lecture 15. Related rates (Textbook: 3.9)
Note: I am not covering all possible types of examples because its just physically impossible due to time constraints. You can get better results when yo
Chapter 3
Rational Functions
Chapter 3 Prerequisite Skills
Chapter 3 Prerequisite Skills
Question 1 Page 146
Answers may vary. A sample solution is shown.
A line or curve that the graph approaches more and more closely. For f(x) =
asymptote is x = 0.
Chap
Chapter 8 Combining Functions
Chapter 8 Prerequisite Skills
Chapter 8 Prerequisite Skills
a)
Pattern A
Question 1 Page 414
Pattern B
Pattern C
b) A: linear increasing one step each time.
B: exponential increasing by a multiple of 2.
C: quadratic increasin
Course Review
Course Review
Question 1 Page 479
a) An even function is symmetric with respect to the y-axis. An odd function is symmetric with
respect to the origin.
b) Substitute x for x in f(x). If f(x) = f(x) for all x, the function is even. If f(x) =
MA103 Mock Midterm
Name:
* Please remember that mock tests are meant as a means of providing an extra set of practice questions
and basis for a review class. Do not study for the midterm based solely on the topics covered by the mock
test! Go back through
MA103 Lab Report 4 - Derivatives Continued
Name:
Student Number:
Fall 2016
1. [4 marks] A new drug has been developed to reduce blood pressure. When x mg (milligrams) of the drug is taken in a day,
the reduction in blood pressure is given to be:
R(x) =
24
MA103 Lab Report 2 - Limit Applications
Would you like this assignment Graded?
YES or NO
Student Number:
Name:
1. [4 marks] Recall Question #2, Lab Report 1, where f (x) =
p
x2
x
Fall 2016
9 4
and a was constant.
a
Determine all horizontal
asymptotes of f
MA103 Lab Report 5 - Derivative Applications
Would you like this assignment Graded?
YES or NO
Student Number:
Name:
Fall 2016
1. [4 marks] Suppose that you invested $12000 on November 1st, 2001 into a GIC (Guaranteed Investment Certicate) paying
an annual
MA103 Lab Report 7 - Antiderivatives and Areas
Would you like this assignment Graded? YES or NO
Student Number:
Name:
Fall 2016
1. [4 marks] Recall Question #2, Lab Report 3, where a manufacturer determined that its "overhead" cost to setup one of their
p
MA103 Lab Report 8
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Student Number:
Name:
1. [5 marks] Suppose y =
Z=4
p
sec4 t
Fall 2016
1dt:
x
(a) Use a property of denite integrals and FTOC Part 1 to nd y 0 :
y=
Z
=4
p
sec4 t
1dt =
x
Z
x
(b) Use FTOC P
MA103 Lab Report 10
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YES or NO
Student Number:
Name:
Fall 2016
1. [5 marks] Recall Question #1, Lab Report 9, where the Gini Index for a country with Lorenz curve L(x) was determined by
Z1
evaluating 200 (x L(x)dx:
0
MA103 Lab Report 9
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Student Number:
Name:
Fall 2016
1. [10 marks] In economics, the Lorenz curve L(x); where 0 x 1; measures the distribution of wealth within an economy.
As an example, if L(0:4) = 0:1; then
MA103 Lab Report 6 - Shapes of Curves
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YES or NO
Student Number:
Name:
Fall 2016
1. [5 marks] In LHospitals calculus writings from 1696, he illustrated the use of his rule using:
2a3 x
lim f (x) = lim
x!a
x!a
(a) Dene