Page3of11 YOUR NAME AND STUDENT #
Problems 116 are multiple choice. Enter the best answer on the ScanTron sheet using an HB or # 2 pencil.
You do not need to show your work. In addition to entering your response on the ScanTron sheet, you
may also wish t
CALC 1000A, Section 006
Second Assignment
Due until Wednesday, October 15, 1pm
Drop box next to MC 255
Instructions
Please read the following instructions carefully:
This assignment is worth 20 marks in total.
There is a bonus question worth 4 marks. It
Introduction to Calculus
Definitions:
1. Secant line: A line that crosses two points on a function.
Slope of AB
f ( xb )f ( xa )
=ARC
xbxa
2. Tangent line: A line that interests a curve (function) at exactly one point.
Slope of the tangent at point P = IR
Derivatives of Sinusoidal Functions
Instantaneous Rates of Change of Sinusoidal Functions
Questions involve identifying the zero, local maximum, and local minimum of a function. The
zero for the slope occurs where the function reaches its peak. The local
Rates of Change and the Number e
Ex 1: Sketch a graph of the function 5x. Then sketch a graph of its derivative.
Ex 2: f(x) = 2x , what is the domain?
Ex 3: Consider the function f(x) =
ex
e x + c . What is the domain, range, and how does the
value of c a
Prerequisite Skills
Secant: A line passing through two different points on a curve
Turning points: The points where a function changes from increasing to decreasing or vice versa
Average rate of change: The rate of change measured over an interval
Extrane
Unit 1: Review Notes
Prerequisite Skills
Evaluating for values within functions: Simply substitute the value into the equation
Factoring: *Always try to common factor first*
If 2 terms: it can be a difference of squares or sum of cubes.
Difference of squa
Unit 1 Review
Prerequisite Skills
Evaluate with the given expression and then factor fully.
f ( x )=x 3 +4 x 2 + x6
a) f(7)
Factor the following:
2
3
2 x 7 x15
8 x 125
m29+6 nn 2
2 ( x2 7 x ) 8 ( x 27 x )120
Simplify and state restrictions if necessary:
5
IB Exploration
Knights Tour in Chess
Purpose: To explore the variance of the Knights tour in a sequence of chessboards. A focus will
be made on a comparison and contrast with the sequence of moves as well as the overall pattern
difference.
The Knights tou
Chapter 2.8
Examples: Find the derivative of the function using the definition of derivative
Chapter 3.1
 The derivative of a constant function will always be 0.
n
n1
 Power rule: x =n x

We can both add and subtract derivatives

Derivative of Natural
Derivative of a Polynomial Function
Example: Determine the slope and equation of the tangent to the curve y=4x5 at x=1/2.
A companys profit p in dollars per month can be expressed as a function of the number of
items manufactorued, x: p(x) = x3 + 32x + 5
Chapter 7 Review
Introduction to Cartesian Vector: Position Vector
Vectors represent a position and the head which is reached by moving xunits to the right and
yunits up. *Need arrow above*
OP=[ x , y ]
Magnitude: OP= x + y
2
2
Vectors can be written
IB Mathematical Studies
Internal Assessment
Examining the Knights Tour
Loudon Herold
Catholic Central High School
IB Candidate Number: 001247008
Exam Session: May 2016
Mathematical Exploration: Knights Tour
Introduction
The Knights Tour is an ancient puz
x
'
x
y=e , y =e . If y =e
f (x)
Special Number: e
then y =f ( x ) e f (x)
'
'
Ex 1: Sketch a graph of the function 5x. Then sketch a graph of its derivative.
Ex 2: f(x) = 2x , what is the domain?
Ex 3: Consider the function f(x) =
ex
e x + c . What is th
AntiDifferentiation and Indefinite Integral
Indefinite Integrals:
f ' ( x ) dx=f ( x ) +c
Rule 1:
xn +1
x dx= n+1 + c
n
6
x 5 dx= x6 +c
Example:
Rule 2:
a x n dx=( n+a 1 )( x n +1 )+ c
Example:
6 x 5 dx=x 6+ c
*For functions where there is multiplyi
Calculus 1000A, Section 003
Fall 2014
Written Solutions Assignment 3
due: Thursday Nov. 13, in class
(two pages!)
1. Show that the function f (x) = x sin(1/x) has innitely many inection points in the open
interval (0, 1).
[Hint: Use the Intermediate Value
Calculus 1000A Mock Exam
Science Soph Team
Congratulations on getting this far in your studies! We hope you find this session useful and that youre not
too stressed for your upcoming mid
Calculus 1000A, Section 003
Fall 2015
Written Assignment 5
due: Monday Dec. 7, in class
1. Evaluate the following sums:
m
n
k=1
l=1
(a)
n
(a)
k
l(l + 1)
2015
k
l=1
k=1
l
.
2. Find the limit:
n
lim
i
n
i=1
n 2
.
2
3. Let f be a function dened (piecewise)
Calculus 1000A, Section 003
Fall 2015
Written Assignment 4
due: Monday Nov. 23, in class
1. A function f is called weakly increasing when x1 < x2 implies f (x1 ) f (x2 ), for any x1 , x2 in
the domain of f . Similarly, f is weakly decreasing when x1 < x2
Calculus 1000A, Section 003
Fall 2015
Written Assignment 3
due: Monday Nov. 9, in class
1. Find the following limits:
x+
(a) lim
x+
x
x+1
1 cos x
.
(b) lim
x0 1 cos( x)
x
2. Find the following limits:
ex
x xln x
ln(1 + ex )
(b) lim
x
x
x
(c) lim+ x .
(a)
Calculus 1000A, Section 003
Fall 2015
Written Assignment 1
due: Monday Oct. 5, in class
1. Find the domain and range of f . Justify your answer.
(a) f (x) = ln(arctan(ex 2015);
p
(b) f (x) = sin( x 4x2 );
x
x
(c) f (x) = ln e +e
.
2
2. (a) Use the deniti
Calculus 1000A, Section 003
Fall 2015
Written Assignment 2
due: Monday Oct. 19, in class
1. Use the Squeeze Theorem to nd the following limits. Justify your answers.
(a) lim
1 x2 sin5 (ln(1 x2 );
x1
ecos(x) ;
x
1
(c) lim x sin
.
x
x
(b) lim sin
x
2. Find
William Morris Davis
STAGE:
: floodplain develops, meandering channel
starts erosion downward and from side to side
William Morris Davis
STAGE:
: V shaped valley, steep slopes, downward and
headward erosion, waterfalls
: floodplain develops, meandering ch
Instructor’s Name (Print)
Thursday, April 21, 2011
Student’s Name (Print)
Student’s signature
THE UNIVERSITY OF WESTERN ONTARIO
LONDON CANADA
DEPARTMENT OF APPLIED MATHEMATICS
Calculus 1000B Final Examination
Code 333
2:00 p.111.  5:00 p.1n.
INSTRUCTIONS
Ca_lculus IDOOA _ CODE 111 Hid3y, October 23, 2009
Midterm Exammatmn Page 1
PART A (50 marks)
NOTE: YOUR ANSWERS TO THE PROBLEMS ON THIS PAGE MUST
BE INDICATED ON THE SCANTRON SHEET.
2 k A1. Find a formula. for the inverse function f‘1(a:), where f(x) =
Calculus lOOOA
Midterm Examination
Friday, October 17, 2008
Page 8
CODE 111
NOTE: YOUR ANSWERS TO THE PROBLEMS ON THIS PAGE MUST
BE INDICATED ON THE SCANTRON SHEET.
A21  A25. For each of the following, choose the letter which labels the graph below
and t
Calculus 1000A
Midterm Examination
Friday, October
Page 3
CODE 111
17, 2008
NOTE: YOUR ANSWERS TO THE PROBLEMS ON THIS PAGE MUST
BE INDICATED ON THE SCANTRON SHEET.
2
A7. Determine lim
x>2marks
~
X+2
=
00

I B: 1
I A: 10 .
I C: 00
+ 7f)
2
A8. If, for
Chapter 8 Review
Equations of Lines and Planes
Equation of a line in 2space is given in a line passing through. A (3, 4) and m= 2/3.
m=[3, 2]
OP=OA + AP, which is then P=u+tm (vector equation of a line)
[ x , y ] =[ 3,4 ] +t [ 3,2 ]
Ex:
t: parameter and
Increasing and Decreasing Functions
Increasing function: A function which over an Interval I (a<x<b) has f(x1) < f(x2) for all pairs
of numbers x1 and x2 in I such that x1 < x2.
Decreasing function: A function which over an interval I (a<x<b) has f(x1) >
Chapter 2
2.2 Limits of Functions
Ex 1.
x 24
f(x) = x2 , x 25, x =2
D(f) = XER
2
x 4 ( x2 ) ( x +2 )
x
2,
=
=x +2
If
x2
( x2 )
Limit: Tendency of y as x > a
lim ( x +4 )=7
Ex 2. x 3
lim f ( x ) =L ( limit maymay not exist )
x a
f(x) = sin
1
2
x
( )
This
2.5 Continuity
Definition: y=f(x) is continuous at a, if and only if
lim f ( x ) =f ( a)
x a
Continuity makes sense only at point in the domain of f.
Definition: f is continuous on an interval I, if f is continuous at all XEI
Ex: f(x) = x, x<0 and x+1, x
Example Exercises for 1.4, 1.5, and Appendix D
Appendix D
1 Convert from degrees to radians for 210o
2
Convert from radians to degrees for
5
12
3
Draw, in standard position for: 315o,
3
rad , and 2 rad
4
4
Find the exact trigonometric ratio for the angle