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x趋近于0,lim(x-arctanx)/x^k=c 求c,k的值
人气:292 ℃ 时间:2020-08-14 04:28:45
解答
=lim (1- 1/(1+x²)) /(k· x^(k-1))
=lim (1+x² - 1) /(k· x^(k-1)) · lim(1/(1+x²) )
=lim (x²) /(k· x^(k-1)) ·1
=lim 1 /(k· x^(k-3))
∴若k≠3,则c=0;
若k=3,则c=1/3
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