7/25/2013 SECOND HOURLY PRACTICE VIII
2013
Maths 21a, O.Knill, Summer
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If
7/11/2013 FIRST HOURLY
Maths 21a, O.Knill, Summer 2013
Name:
Start by writing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If you need additio
7/25/2013 SECOND HOURLY
Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If you need addit
7/11/2013 FIRST HOURLY Practice II
Maths 21a, O.Knill, Summer 2013
Name:
Start by writing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If you
8/8/2013 PRACTICE EXAM I
Maths 21a, O. Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
Do not detach
7/25/2013 SECOND HOURLY PRACTICE VI Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If yo
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 23: Improper integrals
In this lecture, we look at integrals on innite intervals or integrals, where the function can get
innite at some point. These integrals are called improper
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice C
Your Name:
Start by writing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use t
7/25/2013 SECOND HOURLY PRACTICE IV Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If yo
8/8/2013 PRACTICE EXAM V
Maths 21a, O. Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
Do not detach
8/8/2013 PRACTICE EXAM VI
Maths 21a, O. Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
Do not detach
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 10: Worksheet
The chain rule
The rule(f (g(x) = f (g(x)g (x) is called the chain rule.
For example, the derivative of sin(log(x) is cos(log(x)/x.
We have also seen that we can comp
7/25/2013 SECOND HOURLY PRACTICE V Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If you
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 11: Worksheet
Critical points and extrema
In this worksheet we want to nd out which rectangle of xed area
xy = 1 has minimal circumference 2x + 2y.
To solve this problem we have to
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 20: Worksheet
Anti derivatives
Here are some trickier anti derivative puzzles. We still have no integration techniques and must rely on intuition and experiments to nd
the derivati
8/8/2013 PRACTICE EXAM III
Maths 21a, O. Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
Do not detac
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice B
Your Name:
Start by writing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use t
8/8/2013 PRACTICE EXAM VIII
Maths 21a, O. Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work.
Do not deta
7/25/2013 SECOND HOURLY PRACTICE III Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If y
Math 1A: introduction to functions and calculus
Oliver Knill, Spring 2014
4/8/2014: Second midterm practice D
Your Name:
Start by writing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use t
7/25/2013 SECOND HOURLY PRACTICE II Maths 21a, O.Knill, Summer 2013
Name:
Start by printing your name in the above box.
Try to answer each question on the same page as the question is asked. If needed, use
the back or the next empty page for work. If yo
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 13: Worksheet
Hopitals rule
1
What does lHopitals rule say about
exp(2x) 1
?
x0
x
lim
3
2
1
1.0
0.5
0.5
1
1.0
2
Apply lHopitals rule to get the limit of
f (x) =
for x 0.
sin(200x)
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 19: Fundamental theorem
In this lecture we come back to the fundamental theorem of calculus for dierentiable functions. This will allow us in general to compute integrals of functi
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 16: The mean value theorem
In this lecture, we look at the mean value theorem and a special case called Rolles theorem.
Unlike the intermediate value theorem which applied for cont
Math 1A: introduction to functions and calculus
Oliver Knill, 2014
Lecture 34: Calculus and Statistics
In this lecture, we look at an application of calculus to statistics. We have already dened the
probability density function f called PDF and its anti-d
Math S21a: Multivariable calculus
Oliver Knill, Summer 2016
Lecture 9: Partial derivatives
If f (x, y) is a function of two variables, then x
f (x, y) is defined as the derivative of
the function g(x) = f (x, y) with respect to x, where y is considered a
APPROVABLE NON-PROGRAMMABLE
CALCULATOR LIST
Examinations Office
Lvl 3, Jane Foss Russel Bldg
862 78217
[email protected]
CASIO
fx-82 AU
fx-82 AU PLUS
fx-82 AU PLUS II
fx-82 D
fx-82 ES
fx-82 ES PLUS
fx-82 L
fx-82 LB
fx-82 MS
fx-82 NASER
fx-82 PLUS
Pre-exam consultation hours School of Mathematics and Statistics
(all rooms in the Carslaw Building)
Morning
MATH1002 10am-1pm Bob Crossman 707A
MATH1902 10am-12pm Jack Moon 829
Afternoon
MATH1002 2pm-4pm Alexander Fish 712
MATH1011 2pm-4pm Sharon Stephen
CHEATSHEET
MATH1001
Differential Calculus
Complex Numbers
z = a + ib
Where:
z = rcis = r(cos + i sin )
Where r is the modulus |z| and the argument arg z .
University of Sydney
1
2
Polar Form
i2 = 1
Modulus
|z| =
p
a2 + b2
The coecients of the expansion of
8001A SEMESTER 1 2011
THE UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
MATH 1001
DIFFERENTIAL CALCULUS
June 2011 LECTURERS: R. Howlett, X. Liu, N. Saunders, Z. Zhang.
TIME ALLOWED: One and a half hours
Family Name: .
Other Namesr .
This exa