Question
Download Solution PDFIf f(x) is continuous at x = a then \(\rm \displaystyle\underset{x\to a}{\mathop{\lim }}\rm\,f\left( x \right)\)
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
\(\rm \displaystyle\underset{x\to a}{\mathop{\lim }}\rm\,f\left( x \right)\) exists if \(\rm\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a^{+}} f(x)\)
If f(x) is Continuous at x = a
\(\rm\lim _{x \rightarrow a^{-}} f(x)=\lim _{x \rightarrow a^{+}} f(x)=lim _{x \rightarrow a} f(x) = f(a)\)
If f(x) is a continuous function at a point, then it's not necessary that it's inverse will also continuous at the same point.
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