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Came across this question which i have attempted to answer but am sure i have gone wrong somewhere, any help would be appreciated...

Suppose f_{n}(x):R-->R, where f_{n}(x)=x+(1/n) (n belongs to N). Find the pointwise limits of the sequences (f_{n}), (1/n f_{n}) and (f_{n}^{2}). In each case determine whether the convergence is uniform.

Now i managed to get all three as being uniformly convergent and am sure i went wrong somewhere. I am still struggling to understand uniform convergence completely. The pointwise limits i computed were x, 0, x^{2}respectively...sorry i havnt put my working up struggling to use latex.

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# Pointwise Limits and Uniform Convergence Help

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