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Question

If fx=x, x>1x2, x<1, then lim x2fx=____________________________________.

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Solution

fxx; x>1x2; x<1Hence,limx1fx for x<1i.e. L.H.L is given bylimx1-fx =limx1 x2=12=1i.e. L.H.L limx1- fx=1and R.H.L limx1+ fx=limx1 x=1Hence L.H.L=R.H.L i.e.limx1 fx=1

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