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Function convergence proofs

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** Please see the attached file for the complete problem description **

Let f be a function defined on R and, for each natural number n, define the function f_n by....
Decide whether or not you believe the statement is true.

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Solution Summary

This provides examples of proving and disproving statements regarding convergence of a function.

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(a) True
Proof: If f is uniformly continuous, then for any e>0, we can find some d>0, such that for any x, y with |x-y|<d, we
have |f(x)-f(y)|<e. Since 1/n goes to 0<d as n goes to infinity, then we can find some N>0, such that for all
n>N, we have 1/n < d. Thus |(x+1/n) - x| = 1/n < d for any x in R, then we have |f(x+1/n) - f(x)|<e, then
...

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