MathDB

Problem 4

Part of 2012 SEEMOUS

Problems(1)

two integrals, limits of n to infinity

Source: SEEMOUS 2012 P4

6/9/2021
a) Compute lim⁡n→∞n∫01(1−x1+x)ndx.\lim_{n\to\infty}n\int^1_0\left(\frac{1-x}{1+x}\right)^ndx. b) Let k≥1k\ge1 be an integer. Compute lim⁡n→∞nk+1∫01(1−x1+x)nxkdx.\lim_{n\to\infty}n^{k+1}\int^1_0\left(\frac{1-x}{1+x}\right)^nx^kdx.
calculusintegration