Homework For Page 29
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# 1. To show that the limit function f is Lipschitz we have to show that
     there is a constant M>0 s.t. 

     |f(x) - f(y)| \leq M |x - y|, for all x,y in C.

     For simplicity I am using "modulus and C" in place of "metric d and X"
     which makes no difference in the technique.

     Starting from the left hand side add and subtract f_{n}(x) and f_{n}(y).
     Then using triangle inequality, uniform convergence, and Lipschitz
     continuity of f_n's you can prove that f is Lipschitz.
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