This examination has 14 pages including this cover.
UBC-SFU-UVic-UNBC
Calculus Examination
6 June 2013, 12:00-15:00 PDT
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Rules and Instructions
1. Show all your work! Full marks are given only when the answer
is c
DERIVATIVES BASICS
Derivatives Sine and Cosine functions
Derivative
Derivative
Derivative
Derivative
Derivative
Derivative
of
of
of
of
of
of
y
y
y
y
y
y
=
=
=
=
=
=
sin x is y = cos x
cos x is y = -sin x
sin (f(x) is y = cos (f(x) * f(x)
cos (f(x) is y =
Key for the Calculus Challenge Exam in 00-2
1. (a) We can divide out x 1 from both numerator and denominator obtaining:
lim
x 1
x3 1
x2 + x + 1
limx1(x2 + x + 1)
3
= lim 3
=
=
41
2+x+1
3 + x2 + x + 1)
x 1 x + x
x
limx1 (x
4
One can use lHospitals rule to
UBC-SFU-UVic-UNBC Calculus Exam 2005
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Page 2 of 13
[5] 1.
Find the tangent line to the curve y =
x
at the point where x = 1.
1 + x2
Solution:
1 + x2
1
2x
Quotient Rule:
y ( x) =
Evaluation:
m = y (1) =
Line:
y=
x(2x)
(1 + x2 )2
1
(2)
2
22
2
=
1
4
1
UBC-SFU-UVic-UNBC Calculus Exam Solutions, June 2001
UBC Mathematics Resources by Philip D. Loewen
d
(ex tan x) = ex tan x + ex sec2 x.
dx
2000
x
2x + 1/7 .
(b) Chain Rule: f (x) = 2001 x2 +
7
2 x
7
1. (a) Product Rule:
(c) g (t) =
2
4
2
cos(2 ln t), g (t
Key for the 2002 Calculus Challenge Exam
Note: There is no attempt here to describe all possible correct answers. Students sitting the
calculus challenge examination will have used a variety of texts and been exposed to a variety of
teaching styles.
For t
Short Key for 2004 Calculus Challenge Exam
Note: There is no attempt here to describe all possible correct answers. In many cases other
approaches to a question could garner full marks.
For the examiners, apart from the accuracy of the answers, the crucia
SFU UBC UNBC Uvic
Calculus Challenge Examination
June 5, 2008, 12:00 15:00
Host: SIMON FRASER UNIVERSITY
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Student signature
Question
Maximum
1
9
1. Show all your work. Full marks are given only
when the answer is correc
This examination has 15 pages including this cover.
UBC-SFU-UVic-UNBC
Calculus Examination
4 June 2009, 12:00-15:00 PDT
Name:
Signature:
School:
Candidate Number:
Rules and Instructions
1. Show all your work! Full marks are given only when the
answer is c
SFU-UBC-UNBC-UVic
Calculus Challenge Exam Solutions
June 10, 2010, 12:00-15:00
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(please print)
family name
given name
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Question Maximum
Instructions:
1. Show all your work. Full marks are given only when the answer is
correct, and i
UBC-SFU-UVic-UNBC Calculus Exam 2003
[3] 1.
Given f (x) =
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Page 2 of 15
sin x
, nd f (x). (Algebraic simplication is not required.)
ln(x2 + ecos x )
Solution: By the quotient rule and the chain rule,
(cos x) ln x2 + ecos x (sin x)
f (x) =
2x + ecos x