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MATH 20C
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Adam Bowers
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Lecture 8

# MATH 20C Lecture 8: Lecture 8

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University of California - San Diego

Mathematics

MATH 20C

Adam Bowers

Spring

Description

Math 20 C
7 Apr 2017
To day 2. Real Valued Function S
Next
2. 2 Limits and Continuity
Due Friday
Homework
2
2. Real valued unction
A real Value
fuMction of two Variable S
is a rule
at assigns to each pair
a set u the domain) a
in
number.
We usuall
ave the unction a name
f a
we write
f(x,y)
such as
that
the unique real number
or
f as Sign S
to the pair CX, 1)
Notation
the set of real numbers
Number
Line
BlackLoord Lold
TR2 the set all pains E real numbers
Math 20 C 7 Apr 2017 To day 2. Real Valued Function S Next 2. 2 Limits and Continuity Due Friday Homework 2 2. Real valued unction A real Value fuMction of two Variable S is a rule at assigns to each pair a set u the domain) a in number. We usuall ave the unction a name f a we write f(x,y) such as that the unique real number or f as Sign S to the pair CX, 1) Notation the set of real numbers Number Line BlackLoord Lold TR2 the set all pains E real numbers2D Space
3D Space.
Notation for functions
If f is a real valued functon
ot two
var alles, we write
output
input
It u is a subset R2 aud T u rs
the domain
o
f, we can write
us R2 means u is a subset of R
MER means is contained
in R
X is an element o
IR
Element
originally this was an
epsilon.
Note: If the domain u is not specif ed,
they assume u is set of all Cx y)
such that Fay) defined.
Examples
exp x
In this case
we can assume u
In this case u is not all of
Riy) is defmed So long as
2D Space 3D Space. Notation for functions If f is a real valued functon ot two var alles, we write output input It u is a subset R2 aud T u rs the domain o f, we can write us R2 means u is a subset of R MER means is contained in R X is an element o IR Element originally this was an epsilon. Note: If the domain u is not specif ed, they assume u is set of all Cx y) such that Fay) defined. Examples exp x In this case we can assume u In this case u is not all of Riy) is defmed So long ast w such
that
is a geometric ob ect
Order
we frst ident, ty
the bound.
e boundary is where the in equal
IS replace J
with equality
(4,0)
This is the boundar
Curly dee
Notation
du
our domain u is either the inside or
Not Loth)
e outside of this grap
We must find out which of the two it is.
u 2 (x, y) x 112
e origin
this inequality is true
As another example
Is the Point (4,0) in our domain u
Check if he luality is true
t w such that is a geometric ob ec

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