Breaking points and Continuity Definition Evaluation of Limits Continuity Limits Involving InfinitySlide 2
Limit L aSlide 3
Limits, Graphs, and Calculators Graph 1 Graph 2Slide 4
Graph 3Slide 5
c) Find 6 Note: f (- 2) = 1 is not included 2Slide 6
3) Use your adding machine to assess the cutoff points Answer : 16 Answer : no restriction Answer : no restriction Answer : 1/2Slide 7
The Definition of Limit L aSlide 9
Examples What do we do with the x?Slide 10
1/2 1 3/2Slide 11
One-Sided Limits One-Sided Limit The right-hand point of confinement of f ( x ), as x methodologies a , measures up to L composed: in the event that we can make the worth f (x) self-assertively near L by taking x to be adequately near the privilege of a . L aSlide 12
The left-hand farthest point of f ( x ), as x methodologies a , meets M composed: on the off chance that we can make the worth f (x) self-assertively near L by taking x to be adequately near the left of a . M aSlide 13
Examples of One-Sided Limit Examples 1. Given FindSlide 14
More Examples Find the cutoff points:Slide 15
A Theorem This hypothesis is utilized to demonstrate a farthest point does not exist. For the capacity Bu tSlide 16
Limit TheoremsSlide 17
Examples Using Limit Rule Ex. Ex.Slide 18
More ExamplesSlide 19
Indeterminate Forms Indeterminate structures happen when substitution in the utmost results in 0/0. In such cases either calculate or defend the expressions. Notice structure Ex. Element and cross out regular elementsSlide 20
More ExamplesSlide 21
The Squeezing Theorem See GraphSlide 22
Continuity A capacity f is nonstop at the point x = an if the accompanying are valid: f ( a ) aSlide 23
A capacity f is constant at the point x = an if the accompanying are valid: f ( a ) aSlide 24
At which value(s) of x is the given capacity spasmodic? Illustrations Continuous wherever Continuous wherever with the exception of atSlide 25
and Thus F is not cont. at Thus h is not cont. at x=1. F is nonstop wherever else h is ceaseless wherever elseSlide 26
Continuous Functions If f and g are constant at x = a , then A polynomial capacity y = P ( x ) is persistent at each point x. A discerning capacity is persistent at each point x in its area .Slide 27
Intermediate Value Theorem If f is a nonstop capacity on a shut interim [ a , b ] and L is any number between f ( a ) and f ( b ), then there is no less than one number c in [ a , b ] to such an extent that f ( c ) = L . f ( b ) f ( c ) = L f ( a ) a c bSlide 28
Example f ( x ) is constant (polynomial) and since f ( 1 ) < 0 and f ( 2 ) > 0, by the Intermediate Value Theorem there exists a c on [1, 2] to such an extent that f ( c ) = 0.Slide 29
Limits at Infinity For all n > 0, gave that is characterized. Separate by Ex.Slide 30
More ExamplesSlide 33
Infinite Limits For all n > 0, More GraphsSlide 34
Examples Find the points of confinementSlide 35
Limit and Trig Functions From the diagram of trigs capacities we infer that they are persistent all over the placeSlide 36
Tangent and Secant Tangent and secant are constant wherever in their area, which is the arrangement of every genuine numberSlide 37
Limit and Exponential Functions The above chart affirm that exponential capacities are consistent all around.Slide 39
Examples Find the asymptotes of the charts of the capacities
A legitimacy investigation of the Washington Circle congruity of consideration execution measure ...
Organizations that don't recoup inside of 10 days of the calamity are not prone to ... private b ...
calamity will go bankrupt inside of five years. While 85% of Global 2000 endeavors ... Coordinat ...
Mount Fuji Viewed from under Takahashi Bridge. Ca. 1804-1807. Even chuban print. ... the Coast o ...
Achieve Your Technical Peak 2004. Achieve Your Technical Peak 2004. Rearrange your business ... ...
Qualities are the units of legacy that transmit data from folks to posterity ... Basilisk. Solid ...
2. . 3. ICE Custody. ICE confinement is to encourage removalCriminal charges determined before a ...
Alpha Company BATTALION CBRN NCO Continuity Book SSG KILLA BEE. Appointment Orders/ Certi ...
An Introduction to Business Continuity Management. What is Business Continuity Management ? ( ...
Evaluating Limits Analytically. Lesson 1.3. What Is the Squeeze Theorem?. Today we look at ...
Presentations and Challenges. Barclaycard UK - Phil NyeBarclaycard\'s business congruity environ ...
2. Plan. What is COOP?10 Critical ElementsPhases of Plan Development. 3. Crisis Planning: A Nati ...
Lesson Overview. Depict what COOP is and characterize COOP termsDescribe DHS\'s part in COOP pla ...
2. Motivation. Contact InformationCOOP OverviewCOOP Contents COOP Development ProcessDiscussion. ...
An organization\'s congruity capacity
Necessities of the 2006 MSRA. Yearly catch cutoff points and responsibility measures must be act ...
. . . The majority of the methods of math require that capacities ceaseless. A capacity is consi ...