作业帮(n+3*n^1/2)^1/2-(n-n^1/2)^1/3在n趋近于无穷大时的极限值
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(n+3*n^1/2)^1/2-(n-n^1/2)^1/3在n趋近于无穷大时的极限值
(n+3*n^1/2)^1/2-(n-n^1/2)^1/3在n趋近于无穷大时的极限值
(n+3*n^1/2)^1/2-(n-n^1/2)^1/3在n趋近于无穷大时的极限值
直接和(n+3*n^1/2)^1/2比.lim(n->∞)((n+3*n^1/2)^1/2-(n-n^1/2)^1/3)/(n+3*n^1/2)^1/2 =lim(n->∞)1-(n-n^1/2)^1/3/(n+3*n^1/2)^1/2 =lim(n->∞)1-n^1/6*(n^1/2-1)/n^1/4*(n^1/2+3) =lim(n->∞)1-n^1/6*n^1/2/n^1/4*n^1/2 =lim(n->∞)1-1/(n^1/12) =1.所以lim(n->∞)(n+3*n^1/2)^1/2-(n-n^1/2)^1/3 =lim(n->∞)(n+3*n^1/2)^1/2 =∞.
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