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Show that f(x)={(xsinfrac{1}{x},xne0),(0...

Show that `f(x)={(xsinfrac{1}{x},xne0),(0,x=0):}`
is not differentiable x=0

Text Solution

Verified by Experts

`L.H.D.=lim_(hto0)(f(-h)-f(0))/(-h)`
`=lim_(hto0)((-h)sin(-1/h)-0)/(-h)=lim_(hto0)(-sinfrac{1}{h})`
which does not exist.
Similarly R.H.D. does not exist.
So f(x) is not differentiable at x=0
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