Explore BrainMass

Real Analysis : Subsets and Limits

Let f and g be functions defined on a domain A subset or equal to R, and assume lim_x-->c f(x)=L and lim_x-->c g(x)=M for some limit point c of A then,

1-lim_x-->c k f(x)=kL for all k belong to R.

2-lim_x--> [f(x)+g(x)]=L+M

3-lim_x-->c [f(x)g(x)]=LM

4-lim_x-->c f(x)/g(x)=L/M provided M not = 0

Solution Summary

Proofs involving subsets and limits are provided. The solution is detailed and well presented.