n[√(n²+1)-√(n²-1)]=n[√(n²+1)-√(n²-1)][√(n²+1)+√(n²-1)]/[√(n²+1)+√(n²-1)]
=n[(n²+1)-(n²-1)]/[√(n²+1)+√(n²-1)]=2n/[√(n²+1)+√(n²-1)] .分子分母同除以n
=2/[√(1+1/n²)+√(1-1/n²)]
当n趋近于∞时,1/n²趋近于0;
所以极限值为=2/2=1
求极限 lim(n无穷)n【(根号(n^2+1)-根号(n^2-1)】
求极限 lim(n无穷)n【(根号(n^2+1)-根号(n^2-1)】
数学人气:369 ℃时间:2019-09-21 10:34:19
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