Continuity of function | Introduction and Concept in Hindi - 1

A continuous function is a function for which sufficiently small changes in the input result in arbitrarily small changes in the output. Otherwise, a function is said to be a discontinuous function.

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but sir continuity ke lye to L.H.L=R.H.L=value of a function hona chahyia ,, sir choti se confusion h please define..

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sir ,If the function is not defined at a point ,this means that the point is not in its domain .Therefore ,the function is continuous in its domain. For breif explanation you can check the ncert example 9 and 12

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@@MathConnectionDKDinkar It means that ,we need not to check the the continuity of function at that point which is not in its domain. At a point where the function is not defined then there is no mapping of that point in the codomain.

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Good explanation. If a function is discontinuous then why we call it A FUNCTION ANYMORE? it is in the definition of a function that its all domain members MUST have unique image But one of the domain members does not have value then Why call it a function?? If the function is producing Irrational numbers then is it a continuous or discontinuous? if a function outputs Infinity it will be a continuous or discontinuous? if a function outputs a non-terminating value it will be a continuous or discontinuous? if a function outputs indeterminate forms type values is it a continuers or discontinuous?

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Examine the continuity of the function at 𝑥 = 4 .
𝑓(𝑥) = 2𝑥
2 + 1 𝑤ℎ𝑒𝑛 0 ≤ 𝑥 ≤ 2
= 4𝑥 + 1 𝑤ℎ𝑒𝑛 2 < 𝑥 < 4
= 𝑥
2 − 3𝑥 + 2 𝑤ℎ𝑒𝑛 4 ≤ 𝑥 ≤ 6

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