For each n in N, let gn(x) be defined for x => 0 by the formula

gn(x) = nx , 0 <= x <= ( 1/n )

= (1/ nx), 1/n < x

show that lim( gn (x) = 0 ) for all x > 0 and is not uniform on the domain x=> 0, but that it is uniform on a set x => c where c > 0.

 
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