1.

Examine the continuity of the following functions at indicated points.f(x)={(sinfrac{1}{x}if xnea),(0 if x=0 atx=0):}

Answer»

Solution :f(0)=0
`lim_(xto0)sinfrac{1}{X}`does not exist.It oscillates
between -1 and +1
As `lim_(xto0)f(x)=lim_(xto0)sinfrac{1}{x}` does not exist so the FUNCTION f(x) is DISCONTINUOUS at x=0


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