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Examine the continuity of the following ...

Examine the continuity of the following functions at indicated points.
`f(x)={(frac{[x]}{x}ifxne0 at x=0),(0 if x=0):}`

Text Solution

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f(0)=0
L.H.L `=lim_(hto0)|-h|/(-h)`
`=lim_(hto0)h/-h=-1`
`R.H.L==lim_(hto0)|h|/h`
`=lim_(hto0)h/h=1`
As L.H.L. ne R.H.L. ne f(0)`
`therefore` f is discontinuous at x=0
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