Find the value of the constant `k` so that the given function is continuous at the indicated point: `f(x)={k x+1,\ \ \ if\ xlt=picosx ,\ \ \ if\ x >pi` at `x=pi`

Explanation

`lim _{x -> pi^{-}} f(x) =lim _{h -> 0} f(pi-h)`


`text { Let } x=pi-h `


`x -> pi^{-} Rightarrow h -> 0`


`=lim _{h -> 0} K(pi-h)+1[because f(x)=k x+1 text { for } x leq pi`


`=K pi+1 `


`lim _{h -> pi^{+}} f(x) =lim _{h -> 0} f(pi+h)`


`text { Let } x=pi+h `


`x -> pi^{+} Rightarrow h -> 0`


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