- #1
island-boy
- 99
- 0
hello, how do you solve for the limits of the following integrals:
lim as n -> infinity of the integral from 0 to n of [ (1 - x/n)^n times exp(x/2)]
and
lim as n -> infinity of the integral from 0 to n of [ (1 + x/n)^n times exp(-2x)]
Can you solve these using either the monotone convergence theorem or the lebesgue dominated convergence theorem?
and doesn't (1 - x/n)^n and (1 + x/n)^n approach 1 as n approaches infinty? so does that mean I just have to solve the integral of the exponential for both cases from 0 to infinity, which would mean it equals infinity?
lim as n -> infinity of the integral from 0 to n of [ (1 - x/n)^n times exp(x/2)]
and
lim as n -> infinity of the integral from 0 to n of [ (1 + x/n)^n times exp(-2x)]
Can you solve these using either the monotone convergence theorem or the lebesgue dominated convergence theorem?
and doesn't (1 - x/n)^n and (1 + x/n)^n approach 1 as n approaches infinty? so does that mean I just have to solve the integral of the exponential for both cases from 0 to infinity, which would mean it equals infinity?
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