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Real analysis

Let g:A->R and assume that f is a bounded function on A subset or equal to R (i.e there exist M>0 satisfying Absolute value of f(x)<=M for all x belong to A). Show that if lim g(x)=0 as x->c, then g(x)f(x)=0 as x->c as well.

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f(x) is a bounded function on A, then there exists M>0, such that ...

Solution Summary

This is a proof regarding limits and absolute value.