Statement 1: A function f : R → R is continuous at x 0 if and only if lim x → x 0 f ( x ) exists and lim x → x 0 f ( x ) = f ( x 0 ⋅ ) Statement 2: A function f : R → R is discontinuous at

Question

Statement 1: A function f : R → R is continuous at x 0 ​ if and only if lim x → x 0 ​ ​ f ( x ) exists and lim x → x 0 ​ ​ f ( x ) = f ( x 0 ​ ⋅ ) Statement 2: A function f : R → R is discontinuous at x 0 ​ if and only if, lim x → x 0 ​ ​ f ( x ) exists and lim x → x 0 ​ ​ f ( x )  = f ( x 0 ​ . )

TestHub · Accepted Answer

Statement-1 is true. It is the definition of continuity. Statement − 2 is false.

Mathematics - Continuity - Differentiability Question with Solution | TestHub

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