Find the limit of the following:
1.
lim
t 2
t2 4
lim
t 2
(t 2)2
lim
t 2
t2 4
t 2
2.
t 2
3.
t 2
4.
lim
3 x2
x
lim
3 x2
x
lim
3 x2
x
x 0
5.
x 0
6.
x 0
7.
x2 9
lim
x 3
x 3
8.
lim
x 4
9.
16 x2
x 4
1
1
lim 2
x 0 x
x
10.
lim
x2 3
x3 x 2
lim
2 4x3
5x2 3x3
x 0
Lecture 5
Animal Science 2
Dairy Production
GUIDE TO GOOD DAIRY FARMING
PRACTICE
A very good reference
for dairy management in
most production
systems
Published by the
International Dairy
Federation (IDF) and
the Food and
Agriculture
Organization (FAO)
Lecture 7
Animal Science 2
Dairy Production
Feeding
Management
Feeding Management
Cows are ruminants
The stomach of the cow has four chambers,
the largest of which is the rumen
Cows are well adapted to a herbage diet
Cows need water, energy, protein, f
Active Citizenship
and Volunteerism in
UPLB
NSTP 1
Ugnayan ng Pahinungod
MODULE OBJECTIVES
At the end of the session, participants
must be able to:
Define active citizenship
Differentiate among the different
forms/types of school-based public
service in
Lecture 4
Animal Science 2
Dairy Production
Reproduction
The link between reproduction and lactation
has been discussed in previous lectures
Remember that when there is a failure of
lactation, the result will be a failure of the
reproductive process.
W
Lecture 6
Animal Science 2
Dairy Production
Good Dairy Farming Practices
Objectives
Main objective
Safe quality milk is produced from healthy
animals using management practices that
are sustainable from an animal welfare,
social, economic, and environm
CHAPTER 2-MATH 26EF
LIMITS AND CONTINUITY
2.1 The Limit of a Function
2.1 The Limit of a Function
Consider the function f defined by
2
x 4
f ( x)
x 2.
We will investigate the function values (i.e.,
ys or f (x)s) as x gets closer and closer to 2.
NOTE
W
2.3 One-sided Limits
From the definition of a limit of a
function, if we evaluate
lim f x
x a
the function f MUST be defined
on some open interval containing a
except possibly at a itself.
Example. Evaluate lim
x 0
x.
SOLUTION
Let f x x .
The domain of f
2.8 The Intermediate-Value
Theorem
2.8 The Intermediate-Value
Theorem
If a function f is continuous on
(a) iff (b)
the closed interval [a, b] fand
f (ak)
, then for any number
between
and
,
f (b)
there exists at least one number c
between a and b such tha
2.4 Infinite Limits
2.4 Infinite Limits
Def. Let a function f be defined at every
number in some open interval I
containing a, except possibly at the
number a itself. Then f x increases
without bound as x approaches a,
f x if the values of f
written lim
x
2.6 Continuity of a Function at
a number
Continuity of a Function at a Number
A function f is continuous at the number a
if and only if the following three conditions
are satisfied:
i.
f(a) exists
ii.
iii.
lim f x exists
x a
lim f x f a
x a
Remarks
If o
MATH 26 S
Related Rates Supplementary Exercise
1. A rectangular container is 8 ft long, 2ft across the top, and 4ft deep. If water flows in at a
1
rate of 2 ft3 /min, how fast is the surface rising when the water is 1 ft deep? Ans: ft/min
8
2. A liquid is
LIMITS at INFINITY
Limits at Infinity
In this section, we will look into
the behavior of the values of a
function as the value of the
independent variable increases or
decreases without bound.
Limits at Infinity
y k
lim f x k
x
Limits at Infinity
lim f x
2.7 CONTINUITY ON AN
INTERVAL
2.7 CONTINUITY ON AN INTERVAL
Definition
A function f is continuous on
the open interval (a, b) if and only
if f is continuous at every number
between a and b.
A function f is continuous from
the right at a if the following
Do as indicated:
1.
2 if x 1
f(x) 1 if x 1
3 if 1 x
a.
2.
t 4
lim g(s)
s 2
if
if
lim F(x)
x 2
2x 1
h(x)
10 x
a.
7.
lim f(t)
x2
F(x)
8 2x
a.
6.
x 0
s 3 if
g(s)
3 s if
a.
5.
lim f(x)
t 4 if
f(t)
4 t if
a.
4.
x 1
b.
lim f(x)
c. lim f(x)
lim f(x)
c. l
Electronic Mail
(e-mail)
1
E-mail
E-mail messages are sent to the recipients
mail server.
The mail server holds the e-mail message until
you log on to retrieve it.
2
E-mail Account
To use e-mail, you must have an account.
The ISP provides an e-mail accoun
Layout &
Visual Models
Website Layout
Most websites have put their content
in multiple columns.
Multiple columns are created by using
<div> or <table> elements. CSS are
used to position elements, or to create
backgrounds or colorful look for the
pages.
How Internet
Security Works
Field of Network and Internet Security
consists of measures to deter, prevent, detect,
and correct security violations that involve the
transmission of information
Security Violation Example
User A transmits a file to user B. T
CSS
Love of beauty is taste.
The creation of beauty is art.
-Ralph Waldo Emerson
CSS
Cascading Style Sheets
is a style sheet language developed to
control the presentation of markup
language documents
defines how to display HTML elements
Was added to H
Techniques in Network Security
Firewalls
design forced everyone entering or leaving the
castle to pass over a single drawbridge, where
they could be inspected by the I/O police
Firewalls
company can have many LANs connected in
arbitrary ways, but all traf
Big Data and Data Science
Big Data
term that applies to
data or information
that cannot be
handled using
traditional processes
and tools
BIG data problem!
(storage and analyses)
http:/www.nature.com/nature/journal/v498/n7453/full/498255a.html
Chararacteri
INTRODUCTION
TO
THE
Internet
Question
Lets have a moment of silence,
and ask this question to ourselves:
What is the
Internet?
Definition
The Internet is a computer network
consisting of a worldwide network of
computer networks that use the
TCP/IP network
HTML
HTML
HTML (Hyper Text Markup Language)
HTML is a language for describing web
pages.
HTML is a markup language.
The tags describe document content.
HTML documents contain HTML tags
and plain text.
Web
What do we
need to create a
web page?
Text Edi
HTML 5
Creating Web Pages
HTML 5
What is HTML5?
HTML5 will be the new standard for HTML.
The previous version of HTML, HTML 4.01,
came in 1999. The web has changed a
lot since then.
?
HTML 5
New Elements
New Attributes
Full CSS3 Support
Video and Audio
Evolution of Web
World Wide Web
Most prominent part of the Internet
The largest transformable-information construct
introduced by Tim Burners-Lee in 1989
Had went through 5 stages of development:
Web 1.0
Web 2.0
Web 3.0
Web 4.0
Web 5.0
Web 1.0
Tim Burners
Manufacturing sector performance, policy distortions, and past reforms
The Philippine economy as currently constituted cannot on a sustained basis generate
economic development The essential structure of the Philippine economy is still Latin
American rath
Agriculture Sector performance, policy distortions, and past reforms
The Philippine economy as currently constituted cannot on a sustained basis generate
economic development The essential structure of the Philippine economy is still Latin
American rather
Services sector performance and policy
The Philippine economy as currently constituted cannot on a sustained basis generate
economic development The essential structure of the Philippine economy is still Latin
American rather than Asian: a highly ineffici
Structural transformation in the Philippines
The Philippine economy as currently constituted cannot on a sustained basis generate
economic development The essential structure of the Philippine economy is still Latin
American rather than Asian: a highly in
Informal Economy
Operational Definitions1:
The informal sector is broadly defined to include enterprises that fall below the purview of
government regulations. Operationally, the informal sector includes the agriculture and informal
services sectors.
The