Find all points of discontinuity of f, where`f(x)={(sinx)/x , ifx<0x+1, ifxgeq0`

Explanation

`f(0) = 0 + 1 = 1 `
L.H.L. = `underset(x to 0^(-))(lim)f(x) = underset(h to o)(lim)f(0 - h)`
`underset(h to 0)(lim)(sin0 - h)/(0 - h) = underset(h to o)(lim)(- "sin "h)/(h)=1`
R.H.L. `underset(x to 0^(+))(lim)f(x) =underset(h to 0)(lim)f(0 +h)`
`underset(h to 0)(lim)(0+h)+1=0+1=1`
`:'` f(0) = L.H.L. = R.H.L.
`:.` f(x) is contnuous at x = 0 .
at x lt 0, f(x) is continuous .
at x gt 0, f(x) is continous.
`:.` f(x) is continuous for all value of x .