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