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Question

Discuss the continuity and differentiability of the function,
$$f(x)=\begin{bmatrix} \dfrac{x}{1+|x|} & |x|>1 \\ \dfrac{x}{1-|x|} & |x| \leq 1 \end{bmatrix} $$


Solution

$$ \displaystyle \lim_{x\rightarrow 1^-} f(x) = \dfrac{1}{1+1} = \dfrac{1}{2}$$
$$ \displaystyle \lim_{x\rightarrow 1^+} f(x) = \dfrac{1}{1-1}$$ = Doeiut exit
Not continues 1 Not differeatiable


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Mathematics

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