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Differential Calculus

what is meant by contunity of functions

Profile image of sujeesh b
12 Years agoGrade
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1 Answer

Profile image of Jitender Singh
ApprovedApproved Tutor Answer12 Years ago
Ans:
Continuity of a function at a given point means that it should exist at the given point & left hand limit & right hand limit should exist & equal to each other & function value at that point.
Mathematical Explanation:
Let a be point where we need to check the continuity & ‘f’ be the function.
\lim_{x\rightarrow a}f(x)
should exist
Left Hand Limit (LHL):
LHL = \lim_{x\rightarrow a^{-}}f(x)
Right Hand Limit (RHL):
RHL = \lim_{x\rightarrow a^{+}}f(x)
should exist.
Final condition for continuity of f at ‘a’:
\lim_{x\rightarrow a^{-}}f(x) = \lim_{x\rightarrow a^{+}}f(x) = f(a)
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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