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Show that `f(x)=|x|` is continuous at x=0

Answer» `f(x)=|x|={:{(x, xge 0),(-x,x lt 0):}`
Now f(0)=0
`R.H.L = underset(xrarr0^+)(limf(x))=underset(hrarr0)(lim)f(0+h)`
`=underset(hrarr0)(lim)h=0`
`L.H.L=underset(xrarr0^-)(lim)f(x)=underset(hrarr0)limf(0-h)`
`=underset(hrarr0)(lim){-(0-h)}=0`
`therefore` R.H.L = f(0)=L.H.L
`therefore` f(x) is constinuous at x=0 Hence proved.


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