Math 1007, Fall 2006
(These slides replace neither the text book nor the lectures.)
Part IV: Applications of Derivatives & Curve Sketching
27. Maximum and Minimum Values (p. 76-82) 28. Critical Numbers (p. 83-84) 29. Finding Absolute Extrema of a continuo
Test 4, Wednesday,March 18, 2009
MATH 1007 G
Last Name :_ ID #:_
First Name:_
No Calculators are allowed. Show your work Question 1. [5 marks] Use LHospitals rule to evaluate the following limits. For each application, explain why the rule applies. e4x 1
MATHEMATICAL TRIPOS
Monday 6 June 2005
Part II
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in S
MATHEMATICAL TRIPOS
Tuesday 1st June 2004
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four
MATHEMATICAL TRIPOS
Monday 6 June 2005
Part IA
9 to 12
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sectio
MATHEMATICAL TRIPOS
Thursday 29 May 2003
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I. In
Section I, you may attempt all four questions. In S
MATHEMATICAL TRIPOS
Friday 9th June, 2006
Part IB
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four que
MATHEMATICAL TRIPOS
Friday 4 June 2004
Part IB
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Sect
MATHEMATICAL TRIPOS
Monday 31 May 2004
Part II
Alternative B
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
The number of marks for each question is the same.
Additional credit will be given for a substantially complete answer.
W
MATHEMATICAL TRIPOS
Wednesday 8 June 2005
Part IB
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four que
MATHEMATICAL TRIPOS
Tuesday 6th June, 2006
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question
MATHEMATICAL TRIPOS
Friday 2nd June, 2006
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question i
MATHEMATICAL TRIPOS
Friday 28th May 2004
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four q
MATHEMATICAL TRIPOS
Wednesday 2 June 2004
Part IB
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from S
MATHEMATICAL TRIPOS
Tuesday 1 June 2004
Part IB
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Section
MATHEMATICAL TRIPOS
Friday 30 May 2003
Part IA
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I. In
Section I, you may attempt all four questions. I
MATHEMATICAL TRIPOS
Thursday 2 June 2005
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sect
MATHEMATICAL TRIPOS
Thursday 5 June 2003
Part IB
9 to 12
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from Section
MATHEMATICAL TRIPOS
Thursday 9 June 2005
Part IB
9 to 12
PAPER 3
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four questions
MATHEMATICAL TRIPOS
Tuesday 7 June 2005
Part IA
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in
MATHEMATICAL TRIPOS
Wednesday 2 June 2004
Part II
Alternative A
9 to 12
PAPER 2
Before you begin read these instructions carefully.
Each question is divided into Part (i) and Part (ii), which may or may not be
related. Candidates may attempt either or bot
MATHEMATICAL TRIPOS
Thursday 1st June, 2006
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in S
MATHEMATICAL TRIPOS
Monday 5th June, 2006
Part IA
1.30 to 4.30
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question i
MATHEMATICAL TRIPOS
Thursday 9 June 2005
Part II
1.30 to 4.30
PAPER 3
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in
MATHEMATICAL TRIPOS
Monday 2 June 2003
Part II
Alternative A
1.30 to 4.30
PAPER 1
Before you begin read these instructions carefully.
Each question is divided into Part (i) and Part (ii), which may or may not be
related. Candidates may attempt either or b
MATH 1007 Review Problems sin x x . x2
December 2005
Page 1
Prepared by S. Alaca, A.A. Jrai and A.B. Mingarelli a 1. Find lim 2. Find lim
x0
ln(x + 1) x . x0 x2
x
3. Find lim xex . 4. What is lim x2 ln x? +
x0
3 , what is sin ? 5. If 0 and cos = 2 2 3 6.
MATH 1007 A First Name: Student No:
Tutorial #4 Last Name: No Calculators!
Nov 10, 2006
You must show your work for all questions!
1. [4 marks] Use substititution to nd the required integrals: (a) (4 + x2 )10 (2x) dx (b) 2x4 1 (8x3 ) dx
Hint: Set u = 4 +
MATH 1007 A First Name: Student No:
Tutorial #5 Last Name: No Calculators!
Nov 24, 2006
You must show your work for all questions!
1. [4 marks] Find the area between y = 3x2 and y = 3x + 6. (Show algebraically where these 2 functions meet, and give a roug
MATH 1007 A
Tutorial #5
Nov 24, 2006
SOLUTIONS
1. [4 marks] Find the area between y = 3x2 and y = 3x + 6. (Show algebraically where these 2 functions meet, and give a rough sketch of the functions in your answer.) Solution: First we determine where these
MATHEMATICAL TRIPOS
Friday 9 June 2006
Part II
9 to 12
PAPER 4
Before you begin read these instructions carefully.
The examination paper is divided into two sections. Each question in Section II
carries twice the number of marks of each question in Sectio
MATHEMATICAL TRIPOS
Thursday 27th May 2004
Part IA
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four ques
MATHEMATICAL TRIPOS
Tuesday 6th June, 2006
Part IB
9 to 12
PAPER 1
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I. Candidates may attempt at most four questio
MATHEMATICAL TRIPOS
Monday 31st May 2004
Part IA
9 to 12
PAPER 4
Before you begin read these instructions carefully.
Each question in Section II carries twice the number of marks of each question in
Section I.
In Section I, you may attempt all four questi
MATHEMATICAL TRIPOS
Wednesday 4 June 2003
Part IB
1.30 to 4.30
PAPER 2
Before you begin read these instructions carefully.
Each question in Section II carries twice the credit of each question in Section I.
You should attempt at most four questions from S