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Definition of Continuity and Limits:

A continuous function in mathematics is one that does not have any discontinuities, or sudden changes in value.


A function is continuous if it can guarantee arbitrarily tiny changes in its output by confining changes in its input to suitably small amounts.


The limit of a function is a key notion in calculus and analysis that describes how the function behaves near a certain input.

 

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Top things to learn under Continuity and Limits from the online tutor


The concept of limits and continuity is considered to be one of the most crucial ones in calculus. There are many students who even dread the topic. One of the major reasons behind this is how you are introduced to the topic. 


An expert tutor will not only help you strengthen your basics, but also polish your skills to handle the trickiest of concepts. TutorEye has award-winning Math tutors who will teach you-
 

  • Definition of continuity and limits
  • Types of discontinuity
  • One-sided limit
  • Properties of limit
  • Unbounded limits

 

Continuity and Limits Frequently Asked Questions:

Question 1: How is limit and continuity related?

 

A limit is a number that a function approaches when the function's independent variable approaches a certain value.For example,


if the function f (x) = 5x is provided. Then the limit of f (x) as x approaches 2 is 10,i.e, value of f(x)


A function might be continuous or discontinuous in nature.


If a function f with variable x is continuous at the point “a” on the real line if the limit of f(x), as x approaches “a,” is equal to the value of f(x) at “a,” i.e., f(x) = f(a).

 

Question 2: Is limit a continuity?

Continuous functions are denoted by limits. Every function is continuous at every solitary point of its domain, according to the definition of a limit.

 

Question 3: What do you mean by continuity and limit of a function?

A limit is a number that a function approaches when the function's independent variable approaches a certain value.For example, if the function f (x) = 5x is provided.

Then the limit of f (x) as x approaches 2 is 10,i.e, image 2


If the following three requirements are met, a function is said to be continuous at a given point.

f(a) exist

image 3

 

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