Continuity of A Function 2.2. A function f(x) is continuous at x = c if and only if all three of the following tests hold: f(x) is right continuous at.

Slides:

Advertisements

Similar presentations

2 pt 3 pt 4 pt 5pt 1 pt 2 pt 3 pt 4 pt 5 pt 1 pt 2pt 3 pt 4pt 5 pt 1pt 2pt 3 pt 4 pt 5 pt 1 pt 2 pt 3 pt 4 pt 1pt Hole-y Limits! Trig or Treat! Give Piece.

Advertisements

1.5 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

What is a limit ? When does a limit exist? Continuity Discontinuity Types of discontinuity.

Sec 2.5: CONTINUITY. Study continuity at x = 4 Sec 2.5: CONTINUITY Study continuity at x = 2.

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

Continuity and end behavior of functions

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

Continuity When Will It End. For functions that are "normal" enough, we know immediately whether or not they are continuous at a given point. Nevertheless,

1.4 Continuity and One-Sided Limits This will test the “Limits” of your brain!

2.3 Continuity. Most of the techniques of calculus require that functions be continuous. A function is continuous if you can draw it in one motion without.

3.7 Graphing Rational Functions Obj: graph rational functions with asymptotes and holes and evaluate limits of rational functions.

Section Continuity. continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous.

An introduction to limits Limits in calculus : This section gives some examples of how to use algebraic techniques to compute limits. these In cludethe.

Limits. a limit is the value that a function or sequence "approaches" as the input approaches some value.

Objectives: 1.Be able to define continuity by determining if a graph is continuous. 2.Be able to identify and find the different types of discontinuities.

Continuity of A Function. A function f(x) is continuous at x = c if and only if all three of the following tests hold: f(x) is right continuous at x =

2.5 – Continuity A continuous function is one that can be plotted without the plot being broken. Is the graph of f(x) a continuous function on the interval.

A function, f, is continuous at a number, a, if 1) f(a) is defined 2) exists 3)

2.3 Continuity.

Informal Description f(x) is continuous at x=c if and only if there are no holes, jumps, skips or gaps in the graph of f(x) at c.

Review Limits When you see the words… This is what you think of doing…  f is continuous at x = a  Test each of the following 1.

1-4: Continuity and One-Sided Limits

1.4 Continuity  f is continuous at a if 1. is defined. 2. exists. 3.

Section Continuity 2.2.

LIMITS OF FUNCTIONS. CONTINUITY Definition (p. 110) If one or more of the above conditions fails to hold at C the function is said to be discontinuous.

CONTINUITY. A function f(x) is continuous at a number a if: 3 REQUIREMENTS f(a) exists – a is in the domain of f exists.

Limits and Continuity Unit 1 Day 4.

1.3 – Continuity, End Behavior, and Limits. Ex. 1 Determine whether each function is continuous at the given x value(s). Justify using the continuity.

2.4 Continuity Objective: Given a graph or equation, examine the continuity of a function, including left-side and right-side continuity. Then use laws.

Aim: What is the continuity? Do Now: Given the graph of f(x) Find 1) f(1) 2)

DEFINITION Continuity at a Point f (x) is defined on an open interval containingopen interval x = c. If, then f is continuous at x = c. If the limit does.

What is a limit ? When does a limit exist? Continuity Continuity of basic algebraic functions Algebra of limits The case 0/0.

Notes 2.3 – Continuity. I. Intro: A.) A continuous function has no breaks in its domain.

Continuity. What is Continuity? Geometrically, this means that there is NO gap, split, or missing pt. (hole) for f(x) at c. A pencil could be moved along.

基督再來（一）. 經文： 1 你們心裡不要憂愁；你們信神，也當信我。 2 在我父的家裡有許多住處；若是沒有，我就早已告訴你們了。我去原是為你們預備地去。 3 我若去為你們預備了地方，就必再來接你們到我那裡去，我在那裡，叫你們也在那裡， ] ( 約 14 ： 1-3)

Functions and Their Properties Section 1.2 Day 1.

Lesson 61 – Continuity and Differentiability

Ch. 2 – Limits and Continuity

Continuity and One-Sided Limits (1.4)

Ch. 2 – Limits and Continuity

ФОНД ЗА РАЗВОЈ РЕПУБЛИКЕ СРБИЈЕ

1.5 The Limit of a Function.

Continuity Grand Canyon, Arizona.

26 – Limits and Continuity II – Day 2 No Calculator

المبادئ الأساسية للصحة المهنية

Transformations of curves

Слайд-дәріс Қарағанды мемлекеттік техникалық университеті

MATH(O) Limits and Continuity.

.. -"""--..J '. / /I/I =---=-- -, _ --, _ = :;:.

!'!!. = pt >pt > \ ___,..___,..

II //II // \ Others Q.

Пасиви и пасивни операции Активи и активни операции

'III \-\- I ', I ,, - -

I1I1 a 1·1,.,.,,I.,,I · I 1··n I J,-·

Precalculus PreAP/Dual, Revised ©2018

2.3 Continuity Grand Canyon, Arizona.

Selected Problems on Limits and Continuity

26 – Limits and Continuity II – Day 1 No Calculator

Unit 6 – Fundamentals of Calculus

1.4 Continuity and One-Sided Limits This will test the “Limits”

Continuity of Function at a Number

23 – Limits and Continuity I – Day 2 No Calculator

. '. '. I;.,, - - "!' - -·-·,Ii '.....,,......, -,

2.3 Continuity.

Presentation transcript:

Continuity of A Function 2.2

A function f(x) is continuous at x = c if and only if all three of the following tests hold: f(x) is right continuous at x = -5 f(x) is continuous at x = -4 f(x) has infinite discontinuity at x = -3 [i, iii] f(x) has point discontinuity at x = -2 [i, iii] f(x) has infinite discontinuity at x = -1 [i, ii, iii] f(x) is continuous at x = 0

At x = 1 At x = 2 At x = 3 At x = 4 At x = 5 Point Discontinuity [i, iii] Jump Discontinuity [i, ii, iii] Continuous Point Discontinuity [i, (ii), iii]

continuous pt. discontinuity at x = 0 inf. discontinuity at x = 1 pt. discontinuity at x = 3 inf. discontinuity at x = -3 continuous jump discontinuity at x = 2

Find the value of a which makes the function below continuous

Find (a, b) which makes the function below continuous As we approach x = -1 2 = -a + b As we approach x = 3 -2 = 3a + b

Consider the function Find the value of k which makes f(x) continuous at x = 0 Since, if k =1, the hole is filled.