计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]

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计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]lim(x→∞)[x

计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]
计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]

计算极限lim(x→∞)[x-(x^2)ln(1+1/x)]
lim(x→∞)[x-(x^2)ln(1+1/x)] (t=1/x,t→0)
=lim(t→0)[1/t-ln(1+t)/t^2]
=lim(t→0)[t-ln(1+t)]/t^2
=lim(t→0)[1-1/(1+t)]/(2t)
=lim(t→0)t/[(1+t)(2t)]
=1/2