Recent content by BobSun

Limit of an integral 1. Homework Statement Evaluate: the limit as n goes to \infty of \int^{1}_{0} (n^{3/2}x^{5/4})/(1+n^{2}x^{2})dx dx is the lebesgue measure 2. Homework Equations I thought I could use the monotone convergence theorem or the dominated convergence theorem neither work. 3...

Homework Statement Consider the Banach Space l^{1}. Let S={x \in l^{1}|\left\|x\right\|<1}. Is S a compact subset of l^{1}? prove or Disprove.

Homework Statement Let X be a normed linear space. Prove that X is complete if and only if \sum^{\infty}_{n=1} x_{n} converges in X for all sequences (x_{n}) that satisfy \sum^{\infty}_{n=1} \left\|x_{n}\right\|< \infty