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C g n t g f p a s v w e @ b x c l @ a b c o n l i k m v j g e e l f e n w r _About the Author DANIEL SUAREZ is a New York Times bestselling author whose books include Daemon, Freedom TM, Kill Decision, Influx, Change Agent, and Deltav A former systems consultant to Fortune 1000 companies, he has designed and developed missioncritical software for the defense, finance, and entertainment industries2 (a) Define uniform continuity on R for a function f R → R (b) Suppose that f,g R → R are uniformly continuous on R (i) Prove that f g is uniformly continuous on R (ii) Give an example to show that fg need not be uniformly continuous on R Solution • (a) A function f R → R is uniformly continuous if for every ϵ > 0 there exists δ > 0 such that f(x)−f(y) < ϵ for all x

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When we first got introduced a function composition we looked at of actually evaluating functions at a point or compositions of functions at a point what I want to do in this video is come up with expressions that define a function composition so for example I want to figure out what is f of G of X f of G of X and I encourage you to pause the video and try to think about it on your own well G1qs ʫUV L = n mk8v V C ;Solution The solution is similar to the one above By uniform continuity, there exists >0 such that jy xj

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