1 / 41

# Points of confinement and Continuity .

34 views
Category: Art / Culture
Description
Limits and Continuity. Definition. Evaluation of Limits. Continuity. Limits Involving Infinity. Limit. L. a. Limits, Graphs, and Calculators. Graph 1. Graph 2. Graph 3. c) Find. 6. Note: f (-2) = 1 is not involved . 2. 3) Use your calculator to evaluate the limits.
Transcripts
Slide 1

﻿Breaking points and Continuity Definition Evaluation of Limits Continuity Limits Involving Infinity

Slide 2

Limit L a

Slide 3

Limits, Graphs, and Calculators Graph 1 Graph 2

Slide 4

Graph 3

Slide 5

c) Find 6 Note: f (- 2) = 1 is not included 2

Slide 6

Slide 7

The Definition of Limit L a

Slide 9

Examples What do we do with the x?

Slide 10

1/2 1 3/2

Slide 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 a

Slide 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 a

Slide 13

Examples of One-Sided Limit Examples 1. Given Find

Slide 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 t

Slide 16

Limit Theorems

Slide 17

Examples Using Limit Rule Ex. Ex.

Slide 18

More Examples

Slide 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 elements

Slide 20

More Examples

Slide 21

The Squeezing Theorem See Graph

Slide 22

Continuity A capacity f is nonstop at the point x = an if the accompanying are valid: f ( a ) a

Slide 23

A capacity f is constant at the point x = an if the accompanying are valid: f ( a ) a

Slide 24

At which value(s) of x is the given capacity spasmodic? Illustrations Continuous wherever Continuous wherever with the exception of at

Slide 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 else

Slide 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 b

Slide 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 Examples

Slide 33

Infinite Limits For all n > 0, More Graphs

Slide 34

Examples Find the points of confinement

Slide 35

Limit and Trig Functions From the diagram of trigs capacities we infer that they are persistent all over the place

Slide 36

Tangent and Secant Tangent and secant are constant wherever in their area, which is the arrangement of every genuine number

Slide 37

Examples

Slide 38

Limit and Exponential Functions The above chart affirm that exponential capacities are consistent all around.

Slide 39

Asymptotes

Slide 40

Examples Find the asymptotes of the charts of the capacities

Recommended
View more...