Find the value of k for which `f(x)={k x+1` when `xlt=picosx` when `x gtpi`

Explanation

` f(pi) = k pi +1`
R.H.L .` underset(x to pi^(+))(lim) f(x) = underset( h to 0)(lim) f(pi+ h)`
`underset ( h to 0)(lim)cos(pi -h)`
` underset(h to 0)(lim) (-cos h)= - cos 0 =-1`
L.H.L. = `underset(x to pi^(-))(lim)f(x) = underset(h to 0)(lim)f(pi - h)`
`underset(h to0)(lim) k(pi - h) + 1 =k pi+1`
`:' f(x)` is continuous at x = `pi`
`:.` R.H.L. = `f(pi)` = L.H.L.
`rArr kpi + 1 = - 1`
`rArr k = (2)/(pi)`