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 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 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 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 - 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, 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
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, shu@wlu.ca
Lecture 16. LHospitals rule (4.4)
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
t
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
Calculus I
Winter term, 2016
Lecture 14. Exponential model (Textbook: 3.8)
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 book with the no
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
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, shu@wlu.ca
Lecture 11. Logarithmic and implicit differentiation (Textbook: 3.5, 3.6)
Note: I am not covering all possible types of examples because its just physically impossible due to time constraints. Yo
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
Calculus I
Winter term, 2016
Lecture 10. Trig derivatives and chain rule (Textbook: 3.3, 3.4, 3.6)
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 r
Calculus I
Winter term, 2016
Lecture 4. Limit laws and proofs (Textbook: 2.3, 2.4 and bits of 2.6)
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 r
MA103 Lab Report 1 Prep
Page 1
MA103 Lab Report 1 Prep Evaluating Limits
Background Concepts
Limits at a Number (Text: 2.2, 2.3)
To determine lim f (x) we are asking the question:
x!a
As x gets closer and closer to the finite
number a, which single value,
MA103 Lab Report 4 Derivatives Continued
Rules of Dierentiation
Constant Function Rule:
d
[k] = 0, k 2 R
dx
Constant Multiple Rule:
d
[k f (x)] = k f 0 (x), k 2 R
dx
Sum/Dierence Rule:
d
= [f (x)
dx
g (x)] = f 0 (x)
g 0 (x)
d n
[x ] = nxn 1 , n 2 R
dx
Pow
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 Lab Report 1 - Limits
Would you like this assignment Graded?
Name:
Student Number:
YES or NO
Fall 2016
1. [6 marks] Open the le named Graph.pdf under "Lab Report 1" in MyLearningSpace. Use the graph of f (x) to approximate
each of the following. Eac
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, shu@wlu.ca
Lecture 13.
Implicit differentiation and linear approximation (Textbook:
3.5 and 3.10)
Note: I am not covering all possible types of examples because its just physically impossible due to time co
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, shu@wlu.ca
Lecture 12. Implicit differentiation and inverse function derivatives (Textbook: 3.5, 3.6)
Note: I am not covering all possible types of examples because its just physically impossible due to tim
Calculus I
Winter term, 2016
Lecture 17. Mean value theorem (4.2)
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 book with the notes taken
Calculus I
Winter term, 2016
c
2016,
Shengda Hu, shu@wlu.ca
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
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, shu@wlu.ca
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
c
2016,
Shengda Hu, shu@wlu.ca
Lecture 20. Curve sketching and second order derivative (4.3, 4.5)
Note: I am not covering all possible types of examples because its just physically impossible due to time constraints. You can g
MA103 Lab Report 2
Page 1
MA103 Lab Report 2 - Limits Continued
Limits at a Number
To determine lim f (x) we are asking the question:
x!a
As x gets closer and closer to the finite
number a, which single value, if any, does f (x) approach? We can also cons
MA101/103/110 Maple Tutorial
Name:
Student Number:
This worksheet is designed to familiarize you with Maple and some of its common commands. These commands, as well as many
others (which will be shown to you in upcoming labs), will be used throughout the
MA103 Lab Report 3 - Rules of Dierentiation
Derivatives and Dierentiability
A secant is a line which joins two points along a curve. Thus, the slope of the secant joining the
points (a; f (a) and (a + h; f (a + h) along the curve defined by y = f (x) is g
MA103 Lab Report 3 - Derivatives
Name:
Student Number:
1. [4 marks] Consider f (t) =
Fall 2016
2et
:
1 3et
(a) Dene f (t) in Maple.
[Note: Substitute appropriately for ? given that et is exp(t) in Maple.]
f:=(t)->?
(b) Determine f (0); f 0 (t); and f 0 (0
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