1.

`f(x)={{:(kx+1",","यदि ",xlepi),(cosx",","यदि ", x gtpi):}` द्वारा परिभाषित फलन `x=pi` पर |

Answer» `f(x)=kpi+1`
`R.H.L. = underset(xrarrpi^(+))(lim)f(x)=underset(hrarr0)(lim)f(pi+h)`
`=underset(hrarr0)(lim)cos(pi+h)`
`=underset(hrarr0)(lim)(-cosh)=-cos 0=-1`
`L.H.L.=underset(xrarrpi^(-))(lim)f(x)=underset(hrarr0)(lim)f(pi-h)`
`=underset(hrarr0)(lim)k(pi-h)+1=kpi+1`
`because" "f(x), x=pi` पर सतत है
`therefore" "R.H.L.=f(pi)=L.H.L.`
`rArr" "kpi+1=-1`
`rArr" "k=-(2)/(pi)`


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