Show that f(x)= 2x-|x| is continuous …
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Sia ? 6 years, 1 month ago
Let f(x) = 2x − {tex}|x|{/tex}
We have f(x)=2x - {tex}|x|{/tex}
{tex}\Rightarrow f(x)=\left\{\begin{array}{ll}{2 x-(-x)} & {\text { if } x<0} \\ {2 x-(x)} & {\text { if } x>0}\end{array}\right.{/tex}
Continuity at x=0
We have LHL as
{tex}\lim _{x \rightarrow 0^{-}} f(x)=\lim _{x \rightarrow 0^{-}} 2 x+x{/tex}
{tex}\Rightarrow{/tex} 0
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