Examine the continuity of f, where f is defined by`f(x)={sinx-cosx , ifx!=0-1, ifx=0`

Explanation

`f(0)` = -1
and R.H.L. `underset(x to 0^(+))(lim)f(x) =underset(h to 0)(lim)f(0 + h)`
`underset(h to 0)(lim)(sin h - cos h)`
` = sin 0 - cos 0 = -1`
L.H.L. = `underset(x to 0^(-))(lim)f(x) =underset(h to 0)(lim)f(0 - h)`
`underset(h to 0)(lim)sin (-h) - cos (-h)`
` 0 - 1 = -1`
`:'` R.H.L. = f(0) = L.H.L.
`:.` f(x) is continuous at x = 0