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Examine the continuity of the funciton ...

Examine the continuity of the funciton
`f(x)=sinx - cos x, " for "x ne 0`
`=-1" ,for "x =0`
at the point x = 0

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`" L.H.L."=underset(xrarr0^(-))(lim)f(x)`
`=underset(xrarr0^(-))(lim)(sinx - cosx)`
`=0-1`
`=-1`
`" R.H.L."=underset(xrarr0^(+))(lim)f(x)`
`=underset(xrarr0^(+))(lim)(sinx-cosx)`
`=-1`
`underset(xrarr0)(lim)f(x)=-1" (Given)"`
`"L.H.L. = R.H.L. "=underset(xrarr0)f(x)`
So, function is continuous at x = 0.
Hence proved.
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