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Demon117
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Homework Statement
Suppose that [tex]f_{n}[/tex]:R[tex]\rightarrow[/tex]R convergy uniformly to f. If each function [tex]f_{n}[/tex] satisfies [tex]f_{n}[/tex][tex]\rightarrow[/tex] 0 as x[tex]\rightarrow[/tex][tex]\infty[/tex], prove that f[tex]\rightarrow[/tex]0 as x[tex]\rightarrow[/tex][tex]\infty[/tex]. That is show that the limit exists.
Homework Equations
Definition of uniform convergense
Uniform convergence implies pointwise convergence
definition of limits at infinity
The Attempt at a Solution
I have tried to make an estimation using the definition of limits at infinity. I have no idea what I am doing incorrectly but I keep getting that |f(x)|<0 for some reason.
Any advice on this one?