# Uniform and Pointwise Convergence

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QUESTION 1

For each natural number n and each x in [0,1], define

f_n(x)= x/(nx+1)

Find the function f: [0,1] -> R to which the sequence {f_n} converges pointwise. Prove that the convergence is uniform.

QUESTION 2

For each natural number n and each number x, define

f_n(x)= (1-|x|^n)/(1+|x|^n)

Find the function f: R -> R to which the sequence {f_n} converges pointwise. Prove that the convergence is NOT uniform.

https://brainmass.com/math/calculus-and-analysis/uniform-pointwise-convergence-299714

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Question #1

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We have as . If , then we have as . Now set , then point-wisely. Now I show ...

#### Solution Summary

Uniform and Pointwise Convergence is examined.

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