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Show that the function : $f(x)= \left\{ \begin{array}{1 1} |x|, & \quad x\leq2 \\ [x], & \quad x>2 \end{array} \right. $ is continuous [0,2].

1 Answer

Toolbox:
  • Check $ LHL = RHL = f(2)$
  • $ [x] = n \: where\: n \leq x\: n+1\: and \: n \in Z$
LHL $ \lim\limits_{x \to 2^-} | x | = 2$
RHL $ \lim\limits_{x \to 2^+} | x | = 2 $
 
$ f(2) = | 2 | = 2$
$ \Rightarrow f$  is continuous.

 

answered Mar 11, 2013 by thanvigandhi_1
edited Mar 26, 2013 by thanvigandhi_1
 

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