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Problem 2

Part of 2020 SEEMOUS

Problems(1)

SEEMOUS 2020 P2

Source:

5/2/2020
Let k>1k>1 be a real number. Calculate: (a) L=lim⁡n→∞∫01(kxn+k−1)ndx.L=\lim_{n\to \infty} \int_0^1\left( \frac{k}{\sqrt[n]{x}+k-1}\right)^n\text{d} x. (b) lim⁡n→∞n[L−∫01(kxn+k−1)ndx].\lim_{n\to \infty} n\left\lbrack L- \int_0^1\left( \frac{k}{\sqrt[n]{x}+k-1}\right)^n\text{d} x\right\rbrack.
calculus