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Real Analysis - Show E is equicontinuous.

Let E be a set of differentiable functions in C[a,b] with uniformly bounded derivatives; i.e., there exists a number M, independent of f in E,
such that |f'(x)|<=M for all x in [a,b] and all f in E.
Show that E is equicontinuous.

Solution Summary

Equicontinuity is proven. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.