Limits of functions (including one-sided limits)
An intuitive understanding of the limiting process.
Calculating limits using algebra.
Estimating limits from graphs or tables of data.
Asymptotic and unbounded behavior
Understanding asymptotes in terms

Brebeuf College
Calculus Limit - Rules
Mr. Ryan
Rules:
1)
[ f(x) g(x) ] =
2)
c f(x) = c
3)
f(x)
[ f(x) g(x) ] =
g(x)
g(x) 0
4)
5)
f(x)
[ f(x) ] n = [
6)
f(x)
=
f(x) ] n
g(x)
=
f(x) > 0 if n is even
Types:
1) Limits of Constants:
2) Direct Substitution:

Brebeuf College
Calculus Vector Formulas
z
A( ax , ay )
y
a
A( ax , ay , az )
a
B( bx , by )
b
O
b
x
O
Mr. Ryan
B( bx , by , bz )
x
1) a , b Collinear:
a = Kb
2) Comp b a = | a | cos ()
Comp b a =
a a
= | a |2
2)
a b
=
b a
4) Cross ( Vector ) Product
1)
a

Brebeuf College
Calculus - Curve Sketching
Mr. Ryan
To Sketch the Curve y = f ( x )
A) Domain
B) Intercepts
C) Symmetry
D) Asymptotes
- Determine the set of values of x for which f(x) is defined.
- Find the y intercept by setting x = 0 and solving for y (

The 2012 Sun Life Financial
First Name:
Grade
Last Name:
Other:
L
Y
XL
XXL
Date of Birth:
y y y y mm d d
N
A
Gender:
Y
N
E-mail Address:
INSTRUCTIONS:
EXAM:
DIAGRAMS
WORK AND ANSWERS:
A3
A4
A
B3
B4
B
C3
C4
C
ABC
COMC 2012: Final Version
1
COMC 2012 : Fina

The Sun Life Financial
Canadian Open Mathematics Challenge
November 6/7, 2013
STUDENT INSTRUCTION SHEET
General Instructions
1) Do not open the exam booklet until instructed to do so by your
supervising teacher.
2) Take the first five minutes to fill in t

COMC 2013
http:/comc.math.ca/
Ocial Solutions
A1 Determine the positive integer n that satises the following equation:
1
1
1
n
+
+
= 10 .
210 29 28
2
Solution
Adding the left hand side of the given equation with with a common denominator of 210 , we
have,

COMC 2012 Ocial Solutions
1
COMC 2012 Ocial Solutions
by Adrian Tang (adrian.l.tang@gmail.com)
A1 Determine the positive integer n such that 84 = 4n .
Solution: The answer is n = 6.
Solution 1: Note that 84 = (23 )4 = 212 = 46 . Therefore, n = 6.
Solution