lim
x->1 (x^(1/3)-1)/(x-1)
lim x->1
2012-04-25 6:31 am
回答 (2)
2012-04-25 6:43 am
✔ 最佳答案
lim x→1 (∛x - 1) / (x - 1)
= lim
x→1 (∛x - 1) / [(∛x - 1) (∛x² + ∛x + 1)]
= lim
x→1 1 / (∛x² + ∛x + 1)
= 1 / (∛1² + ∛1 + 1)
= 1/3
2012-04-25 11:27 pm
By L'Hospital Rule,
lim (x->1) [x^(1/3) -1]/(x-1)
= lim (x->1) (1/3)x^(-2/3)
= 1/3
lim (x->1) [x^(1/3) -1]/(x-1)
= lim (x->1) (1/3)x^(-2/3)
= 1/3
收錄日期: 2021-04-21 22:24:22
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