Summary Calculus, perfect handwriting notes for you. With planty examples and explanation. ISBN: 9781938168079 MAT135 (MAT135)
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Course
MAT135 (MAT135)
Institution
University Of Toronto (U Of T
)
Book
Calculus
Perfect handwriting notes. Great help for your calculus. It varies from basic formulas and concepts to exciting questions to thoroughly explained examples. I hope this note will help students who need the summary or the examples to understand calculus. Don't forget to have a look at my other course...
Questions and detailed answers on Parametric equations and polar coordinates
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)
Maths
MAT135 (MAT135)
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135
NAT
crawford
, Section 1. I
or
→A
FUNCTION :
A function consists of a set of inputs ( the domain ) i
a set of outputs ( the range ] ,
and a rule for assigning each input to
exactly
one output
☒¥5T horizontal
.
line
µµ ¥4
:
:
Vertical line Two ineeoseoes function
→ one
-
to -
one
if fix , ) -1-1-1×2 ] When Xi =/ X2
(V ) ( X )
{
notation interval noeaiaion
see -
builder notation
D= 15 x )
{
,
D= {✗ 1 a > 5. HER } or D=
{ ✗ c- r I ✗ > 5
} or D= { XIX 53 >
Composite Functions :
If f- and g are functions and
the range of f is a subset of the domain of g ,
then their composition
go f is the function ego f) CXI =
gcfcxs )
If +
g) IX) =
f- Cx) + guy
ftp.gcxlfog-fcglxy-g
f. g =
,Section i. 2
FUNCTIONS :
There are a main to
ways represent
functions .
A table of value
{ A
A
A
formula
graph
word description
Piecewise Defined Functions ( PDF)
-
: is a function
defined by different formulas different parts
of on its domain
°
if
/
§
✗ ✗< I
fcx , = •
= closed
2- ✗ if I E ✗ <3
.
✗ -1 if • ex ⑤
open
=
absolute value function
f-CX ) = 1×1 -
, Mathematical modelling :
* The process life problem formula equations
of translating a real -
into .
* Tries to predict future events .
* Mathematical analysis of a problem / situation .
* using data & observation
/analysing to find outcomes .
* Not always 100% accurate
* Aim for useful enough
it to be accurate enough to be but simple
,
to make computations
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