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What Happens to a Function F (X) at X = A, If Lim X → a F (X) = F (A)?

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Question

What happens to a function f (x) at x = a, if  

\[\lim_{x \to a}\] f (x) = f (a)?
Sum
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Solution

 if \[f\left( x \right)\]  is a function defined in its domain such that 

 \[\lim_{x \to a} f\left( x \right) = f\left( a \right)\], then 

\[f\left( x \right)\]  becomes continuous at 
\[x = a\].
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Chapter 8: Continuity - Exercise 9.3 [Page 41]

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R.D. Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 8 Continuity
Exercise 9.3 | Q 2 | Page 41

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