A function f x is continuous at a point x - a- then which of the following is incorrect-A- fa-0-0001-fa-0-0001B- fa-lim - fxC- lim - fx-lim - fxD- lim h - 0 fa-h x - a-fa

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Byju's Answer

Standard XI

Mathematics

Single Point Continuity

A function f ...

Question

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

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Solution

The correct option is A

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

The condition are

A finite limit exist for the function at the given point, $lim x \to a f (x)$

$lim x \to a f (x) = f (a)$

These conditions are represented by option b,c,d. f(a+0.0001)=f(a-0.0001) doesn't mean thatt

limit exist and for a continuous function this may not be the ease. The $Δ$ in $f (a + Δ)$ or $f (a - Δ)$ should be infinitesimally small, but 0.0001 is very large compared to such a desired value.

Hence (a) is incorrect.

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