高数 极限问题 图中5,7,9,11,13题求解答
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lim(n→∞) (1/n) Σ(i=1→n) (1 + i/n)^(1/3)
= ∫[1→2] x^(1/3) dx
= x^(1 + 1/3)/(1 + 1/3) |[1→2]
= (3/4)x^(4/3) |[1→2]
= (3/4)2^(4/3) - (3/4)(1)
= 3/2^(2/3) - 3/4
= ∫[1→2] x^(1/3) dx
= x^(1 + 1/3)/(1 + 1/3) |[1→2]
= (3/4)x^(4/3) |[1→2]
= (3/4)2^(4/3) - (3/4)(1)
= 3/2^(2/3) - 3/4
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