Solution-Evaluate lim sup ek, Evaluate lim sup Ek

Evaluate lim sup ek

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Reference no: EM131046

1. Evaluate lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even.

2. Show that the set E = {x in R^2 : x1, x2 in Q} is dense in R^2.

3. let r>0 and S={x in R^3:(x1)^2+(x2)^2+(x3)^2<(r)^2} show that diam S=2r.

4. let x=(x1,...xn) in Rn.show that (? k=1,n xk)^2<=n|x|^2.

Reference no: EM131046

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