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Question

A function f(x) is continuous at a point x=a, then which of the following is incorrect.


A

f(a+0.0001)=f(a0.0001)

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B

f(a)=limxa+f(x)

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C

limxaf(x)=limxa+f(x)

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D

limh0f(ah)=f(a)

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Solution

The correct option is A

f(a+0.0001)=f(a0.0001)


Option b. ,c. ,d. are correct. This deals with the condition by which we say a function is continuous.

The condition are
1. A finite limit exist for the function at the given point, limxaf(x)

2. limxaf(x)=f(a)

These conditions are represented by option b. ,c. ,d.
f(a+0.0001)=f(a0.0001) doesn't mean that limit exist and for a continuous function this may not be the case. The Δ in f(a+Δ) or f(aΔ) should be infinitesimally small, but 0.0001 is very large compared to such a desired value.

Hence (a) is incorrect.


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