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# pointwise limit

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For each natural number n and each number x in (-1,1), define
f_n (x)=&#8730;(x^2+1/n)
and define f(x)=|x|. Prove that the sequence {f_n} converges uniformly on the open interval (-1,1) to the function f. Check that each function f_n is continuously differentiable, whereas the limit function f is not differentiable at x=0.

Please give full proof and as many details as you can. See attachment for the problem with full equations.

https://brainmass.com/math/real-analysis/analysis-uniform-convergence-302856

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For each natural number and each number in , define

and define . Prove that the sequence converges uniformly on the open interval to the function . Check that each ...

#### Solution Summary

Help to calculate the pointwise limit is given.

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