Share
Explore BrainMass

Lebesgue Measures, Integrals and Limits : Let f_n(x) = n^1/2 * x * e^(-n*x^3), for n = 1,2,3... (i) Find the maximum value assumed by f_n in the interval [0,1] and (ii) Find Lim (n -> infinity) of...

Let f_n(x) = n^1/2 * x * e^(-n*x^3), for n = 1,2,3...
(i) Find the maximum value assumed by f_n in the interval [0,1].
(ii) Find Lim (n -> infinity) of integral from 0 to 1 of (f_n(x))dx.

All integrals here are with respect to Lebesgue measure. Please justify every step
and claim.
e here is the exponential function.

Solution Summary

Lebesgue Measures, Integrals and Limits are investigated. The solution is detailed and well presented.

$2.19