THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
MAST10006
Calculus 2
SEMESTER 1, 2014
This compilation has been made in accordance with the provisions of Part VB of the copyright act for the
teaching purposes of the University.
This b

Answers to MAST10006 CALCULUS 2 Exam
Semester 1, 2013
These are not full solutions, just answers and some indications of methods.
1. (a) Use LHpitals rule to get 0.
o
(b) The limit does not exist as sin(2x) oscillates.
2x + sin x
2x
sin x
(c) Write lim
=

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
MAST10006
Calculus 2
Lecture Notes
This compilation has been made in accordance with the provisions of Part VB of the copyright act for the teaching purposes of the University.
This book

Answers to MAST10006 CALCULUS 2 Exam
Semester 2, 2013
These are not full solutions, just answers and some indications of methods.
1. (a) Use the sandwich theorem to get 0.
(b) Multiply the numerator and denominator by
t2 4t + t and let t to get 1 .
2
log

MAST10006 Calculus 2, Semester 2 2015, Assignment 2 Solutions
Marks Legend: Marks are awarded for reasoning/justification R , method M , correct answer A
and notation N . There is one notation mark for each question. You will only receive this mark if all

MAST10006 Calculus 2, Semester 2 2015, Assignment 3 Solutions
Marks Legend: Marks are awarded for reasoning/justification R , method M , correct answer A
and notation N . There is one notation mark for each question. You will only receive this mark if all

The University of Melbourne
Department of Mathematics and Statistics
Semester 2 Examination 2013
MAST10006 Calculus 2
Examination Duration: 3 hours
Reading time allowed: 15 minutes
This paper has 7 pages, including this cover sheet.
Exams Papers with Comm

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
SEMESTER 1, 2009
620-155 CALCULUS 2
Exam duration 7 Three hours
Reading time 15 minutes
This paper has 7 pages, including this cover sheet.
Instructions to Invigilators:
Initially, stude

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
SEMESTER 2, 2010
MAST10006 (620155) CALCULUS 2
Exam duration 7 Three hours
Reading time 7 15 minutes
This paper has 6 pages, including this cover sheet.
Exam Papers with Common Content:

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
SEMESTER 1, 2008
620155 CALCULUS 2
Exam duration W Three hours
Reading time _ 15 minutes
This paper has 7 pages, including this cover sheet.
Instructions to Invigilators:
Initially, stud

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
SEMESTER 1, 2010
620155 CALCULUS 2
Exam duration ~ Three hours
Reading time 15 minutes
This paper has 6 pages, including this cover sheet.
Instructions to Invigilators:
Initially, studen

THE UNIVERSITY OF MELBOURNE
DEPARTMENT OF MATHEMATICS AND STATISTICS
SEMESTER 2, 2008
620-155 CALCULUS 2
Exam duration Three hours
Reading time 15 minutes
This paper has 7 pages, including this cover sheet.
Instructions to Invigilators:
Initially, student

-~-~-
The University of Melbourne
Semester 2 Assessment 2013
School of Physics
PHYC-I0004
Physics 2: Physical Science & Technology
Reading time:
Exam Duration:
This paper has:
15 minutes
3 hours
12 pages + formula sheet
Authorised Materials:
Instru~tions

School of Mathematics and Statistics
MAST10006 Calculus 2, Semester 2 2015, Assignment 4
Student Name
Student Number
Tutors Name
Tutorial Day/Time
Submit your assignment to your tutors MAST10006 assignment box
before 4pm on Monday 12th October.
This assig

Answers to MAST10006 CALCULUS 2 Exam
Semester 2, 2014
These are not full solutions, just answers and some indications of methods.
1. (a)
i. Use the sandwich rule with bounds 2 |x 2 | < x 2 arctan x1 < 2 |x 2 |
2
to get limit 0.
ii. Combine terms over comm

!
Semester 2 Assessment, 2015
School of Mathematics and Statistics
MAST10006 Calculus 2
Writing time: 3 hours
Reading time: 15 minutes
This is NOT an open book exam
Common content with: MAST10009 Accelerated Mathematics 2
This paper consists of 7 pages (i

Student number:
The University of Melbourne
Semester 1, 2014 Assessment
Department of Mathematics and Statistics
MAST10006 Calculus 2
Reading Time:
15 minutes
Writing Time:
3 hours
Open Book Status: Closed book
This paper has 7 pages including this page.

School of Mathematics and Statistics
MAST10006 Calculus 2, Semester 2 2015, Assignment 3
Student Name
Student Number
Tutors Name
Tutorial Day/Time
Submit your assignment to your tutors MAST10006 assignment box
before 4pm on Wednesday 23rd September.
This

!
Semester 2 Assessment, 2015
School of Mathematics and Statistics
MAST10006 Calculus 2
Writing time: 3 hours
Reading time: 15 minutes
This is NOT an open book exam
Common content with: MAST10009 Accelerated Mathematics 2
This paper consists of 7 pages (i

lOMoARcPSD
Exam Sem 2, 2011 Questions and answers.pdf
Calculus 2 (University of Melbourne)
Distributing prohibited | Downloaded by ? ? ([email protected])
lOMoARcPSD
The University of Melbourne
Department of Mathematics and Statistics
Semester 2 Exami

MAST10006 Calculus 2
Tutorial 4
Note: You are expected to provide complete explanations for your answers using correct
notation throughout.
1. Evaluate the following limit: lim tanh x
x
2. If cosh x =
5
what are the possible values of:
3
(a) sinh x
(b) ta

School of Mathematics and Statistics
MAST10006 Calculus 2, Semester 2 2015, Assignment 1
Student Name
Student Number
Tutors Name
Tutorial Day/Time
Submit your assignment to your tutors MAST10006 assignment box
before 4pm on Monday 17th August.
This assign

!
Semester 1 Assessment, 2015
School of Mathematics and Statistics
MAST10006 Calculus 2
Writing time: 3 hours
Reading time: 15 minutes
This is NOT an open book exam
This paper consists of 5 pages (including this page)
Authorised materials:
No materials a

Answers to MAST10006 CALCULUS 2 Exam
Semester 1, 2014
These are not full solutions, just answers and some indications of methods.
1. (a) Use LHopitals Rule to get limit 0.
(b) Use continuity of log
to take limit inside the logarithm. Then multiply numera

Answers to MAST10006 (620-155) CALCULUS 2 exam
Semester 2, 2010
These are not full solutions, just answers and some indications of methods.
2
(divide numerator and denominator by x11 )
5
(ii) 0 (sandwich rule)
1
(iii) (multiply numerator and denominator b

Answers to 620-155 CALCULUS 2 exam
Semester 1, 2010
These are not full solutions, just answers and some indications of methods.
1. (a) (i) 5 (factorise numerator and denominator)
(ii) 4 ( multiply numerator and denominator by t2 + t + t )
(iii) 0 ( by lHo

School of Mathematics and Statistics
MAST10006 Calculus 2, Semester 2 2016, Assignment 4
Student Name
Student Number
Tutors Name
Tutorial Day/Time
Submit your assignment to your tutors MAST10006 assignment box
before 4pm on Monday 10th October.
This assig

School of Mathematics and Statistics
MAST10006 Calculus 2, Semester 2 2016, Assignment 3
Student Name
Student Number
Tutors Name
Tutorial Day/Time
Submit your assignment to your tutors MAST10006 assignment box
before 4pm on Monday 19th September.
This ass

MAST10006 Calculus 2
Tutorial 4
Note: You are expected to provide complete explanations for your answers using correct
notation throughout.
1. Evaluate the following limit: lim tanh x
x
2. If cosh x =
5
what are the possible values of:
3
(a) sinh x
(b) ta

Chapter 1
Applications of First Order Equations
1.1
1.1.1
Commercial Applications
Continuously Compounded Interest
If $1000 is invested at 6% p.a. interest compounded annually, then after 1 year the investment
is worth $1000 1.06, after 2 years [$1000 1.0

Student ID
!
Semester 1 Assessment, 2016
School of Mathematics and Statistics
MAST10006 Calculus 2
Writing time: 3 hours
Reading time: 15 minutes
This is NOT an open book exam.
This paper consists of 5 pages (including this page).
Authorised materials:
N

MAST10006 Calculus 2
Tutorial 2
Note: You are expected to provide complete explanations for your answers using correct notation
throughout.
1. Can I get started! Match the type of the limit and the first step in finding the limit to the
given examples in

1. Consider the surface
z = f (x, y) = log
(a) Find the x, y and z intercepts.
(b) Find and sketch the level curves for z =
p
x2 + y 2 .
1, 0, 1.
(c) Find and sketch the cross-sections of the surface in the x-z plane and the y-z plane.
(d) For which value