Working definition of continuity , Mathematics

Assignment Help:

"Working" definition of continuity

A function is continuous in an interval if we can draw the graph from beginning point to finish point without ever once picking up our pencil. The graph has just two discontinuities as there are only two places where we ought to be picked up our pencil in sketching it.

In other terms, a function is continuous if its graph contains no holes or breaks in it.

For several functions it's simple to find out where it won't be continuous.  Functions won't be continuous where we contain things such as division by zero or logarithms of zero.  Let's take a rapid look at an instance of determining where a function is not continuous.

Example   Find out where the function below is not continuous.

                            h (t ) =4t + 10 / t 2 - 2t -15

Solution

Rational functions are continuous everywhere apart from where we have division by zero.  Thus all that we have to determine where the denominator is zero. That's simple enough to find out by setting the denominator equivalent to zero & solving.

                                        t 2 - 2t -15 = (t - 5) (t + 3) = 0

Thus, the function will not be continuous at t=-3 & t=5.

A nice consequence of continuity is the given fact.

Fact 2

If  f ( x ) is continuous at x = b and 446_limit28.pngthen,

1266_limit29.png


Related Discussions:- Working definition of continuity

Explain measurement conversions in details, Explain Measurement Conversions...

Explain Measurement Conversions in details? The following tables show measurements of length, distance, and weight converted from one system to the other. Length and Distanc

Developing an understanding ones tens and more, DEVELOPING AN UNDERSTANDING...

DEVELOPING AN UNDERSTANDING :  The other day I was showing the children's book '203 Cats' to my 7-year-old niece. She had recently learnt how to write large numerals in her school

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

Acid solution, A 90% acid solution is mixed with a 97% acid solution to obt...

A 90% acid solution is mixed with a 97% acid solution to obtain 21 litres of a 95% solution. Findout the quantity of every solutions to get the resultant mixture.

Lesson 3.5 skills practice, Noah is renewing a magazine subscription. one p...

Noah is renewing a magazine subscription. one package offers to renew the magazine for 3 years for 26$. A second package offers to renew the magazine for 5 years for $38

Create a table with the number of components of each size, Look on the web ...

Look on the web for a data base that can be converted to an undirected graph.  For  example, in Science there is a data base of proteins and their interactions.  Each protein can b

Sample of proportion program., help me with how to write sample of proport...

help me with how to write sample of proportion using visual basic

What is the vertex form for a quadratic equation, What is the Vertex Form f...

What is the Vertex Form for a Quadratic Equation ? The vertex form for a quadratic function is as follows: f(x) = a(x - h) 2 + k The graph of this function Is a parabola whos

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd