Is the function defined by $f (x) = | x |$ , a continuous function?

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Solution

$\begin{matrix} f (x) = | x | i s c o n t i n u o u s \Rightarrow f (x) = | x | = {\begin{matrix} x & x ⩾ 0 - x & x < 0 \end{matrix} f (0) = 0 \Rightarrow {lim}_{x \to 0^{+}} f (x) = {lim}_{x \to 0} f (0 + n) = 0 \Rightarrow {lim}_{x \to 0^{-}} f (x) = {lim}_{x \to 0} (0 - h) = {lim}_{x \to 0} | 0 - h | = 0 H e n c e f (0) = f (0^{+}) = f (0^{-}) = 0 \end{matrix}$

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