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Question

If a function f(x) is defined in x ϵ [a, b], then f(x) is continuous at a if


A

limxaf(x)=limxa+f(x)=f(a)

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B

limxa+f(x)=f(a)

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C

Function will be continuous in any case

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D

Function will be discontinuous in any case

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Solution

The correct option is B

limxa+f(x)=f(a)


For a function f(x) defined in [a, b]. the condition for continuity is that the RHL at a should be = f(a), since there are no value for f(x) for x< a. for the same reason we cant take the left hand limit of the function at x = a.


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