Let $f(x) = \left\{ \begin{array}{r} 1,\ when\ x\ is\ rational \ 0,\ when\ x\ irrational \end{array} ight.\$, then $\lim_{x ightarrow 0}{f(x)}$ is

Question

Let $f(x) = \left\{ \begin{array}{r} 1,\ when\ x\ is\ rational \ 0,\ when\ x\ irrational \end{array} ight.\$, then $\lim_{x ightarrow 0}{f(x)}$ is

Dr. Abubacker · Accepted Answer

(b)
LHL$= \lim_{x \rightarrow 0^{-}}{f(x)} = \lim_{h \rightarrow 0}{f(0 - h)} = 1$
[$\because(0 - h)$ is rational]
RHL$= \lim_{x \rightarrow 0^{+}}{f(x)} = \lim_{h \rightarrow 0}{f(0 + h)} = 1$
[$\because(0 + h)$ is rational]
Hence, LHL=RHL=1

Q. Let $f(x) = \left\{ \begin{array}{r} 1,\ when\ x\ is\ rational \\ 0,\ when\ x\ irrational \end{array} \right.\$, then $\lim_{x \rightarrow 0}{f(x)}$ is

Explanation

Reviewed by Dr. Abubacker

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