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Question

limx2tanπxx2+Ltx(1+1x2)x=bπ+a Find a+b

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Solution

limx2tanπxx2+limx(1+1x2)x
=limx2tan(πx2π)x2+limx(1+1x2)x2.1x
=limx2πtan(pi(x2)π(x2)+elimx1x=π+e0=π+1
a+b=1+1=2

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