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Continuity And Differentiability

Question

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Test the continuity of the function f(x) at the origin :
$straight f left parenthesis straight x right parenthesis equals open curly brackets table attributes columnalign left end attributes row cell fraction numerator open vertical bar straight x close vertical bar over denominator straight x end fraction comma space space space space straight x not equal to 0 end cell row cell space space space 1 space space space space comma space space space space straight x equals 0 end cell end table close$

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