1051 Assignment 2
Due Thursday 1st April 2010, 2 pm
Write your name, student number, tutors name, tutorial group (T1, T2, . . . ) and tutorial time clearly on the top of the front page of your assignment. Staple the pages of your assignment. Locate the bo
2.9 Composition of Functions
If
and
are two functions, the composition of
and , denoted
(
, is given by:
)
This basically means you apply the function to some input first, then apply function . This
means that the domain (inputs) of
are given by the possi
Chapter 2 - Functions
2.1 Notation
The notation
some input from
means maps from into . In other words, the function transforms
into an output which is in the set .
2.2 Definition: Function, Domain, Range
A function
is a rule which takes every element whic
A word of warning if Series B converges, but every term in Series A is larger then it could
very well diverge (or simply converge to a higher value). This test would tell you nothing!
Similarly if Series B diverges, but every term in Series A is smaller t
Taking the limit:
7.4 Theorem: p-test
For
, the p-series
Is convergent if
(since each term will get smaller and smaller), and divergent if
.
Actually, if
, this reduces to the harmonic series. If you wanted to change the base, you
could do so quite easily
1051 Assignment 2
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Due Monday 29th August 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late
MATH1051
Assignment 4
All questions must be submitted by 3 pm on Thursday 20 October. Assignments can be submitted at your
tutorial or to the assignment submission machine (3rd floor, Priestley Building #67). You do need a cover
sheet which will be emaile
1051 Assignment 3
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Due 19th September 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late assi
1051 Assignment 3
?
?
?
?
?
?
Due 19th September 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late assi
1051 Assignment 2
?
?
?
?
?
?
Due Monday 29th August 2016, 3 pm
Make sure you include your personalized cover page with this assignment.
Staple the pages of your assignment.
Submit your assignment on level 3 of building 67 by the indicated deadline.
Late
This is true no matter what value of you have. You simply cant get a negative output from ,
since a negative exponent simply makes the output smaller, not positive. Accordingly, you cant
input a negative number into
its not a possible output to the norma
Chapter 7 - Series
7.1 Infinite Sums (Notation)
Recall that an infinite sum is represented as:
The lower bound (
) may vary.
Notice that a sequence is simply a list of terms
but a series is a sum
.
7.2 Motivation
Math is generally fairly dry. So you know
Chapter 6 Derivatives
Derivative has a stigma to it, since its part of calculus and calculus is regarded as difficult.
Derivatives simply involve rates of change (which are slopes on a graph).
6.1 Tangents
Lets say we want to determine the tangent line at
6.12 Definition: Increasing / Decreasing
A function
is strictly increasing if:
A function
is strictly decreasing if:
6.13 Increasing / Decreasing Test
If
, then is strictly increasing on
to values getting larger (more positive).
. The positive rate of cha
6.8 Derivative of Inverse Function
Useful examples here, but mostly more practice. We do, however, have some more handy
derivatives (and by handy, we mean that itll probably be on your exams):
6.9 LHpitals Rule
I believe this is pronounced Le Pee-Tals the
Chapter 5 - Continuity
5.1 Definition: Continuity
We say that a function
is continuous at a point
if:
exists
The limit at
exists
Picture a graph of the function. The first criterion ensures theres a point somewhere on the
graph when
. The second criterion
Chapter 1 - Numbers
1.1 Number Systems
Set of natural numbers
. Subset of , and .
: Set of integers
. Subset of and .
: Set of rational numbers, which are of the form where
and
. Subset of .
: Set of real numbers represented by a finite or infinite decim
MATH1051
CALCULUS
AND
LINEAR ALGEBRA I
Semester 1, 2016
Lecture Workbook
How to use this workbook
This book should be taken to lectures, tutorials and lab sessions. In the lectures, you will be expected
to fill in the blanks in any incomplete definitions,