Please solve 2(a) For n e N, define fn : [-1, 1] → [0, 1] by fn(x) = (1 – x2)". For all 8 e (0,1), defineIs = [–1, –ô] U [8, 1].(a)(Ъ)Prove that (fn)nEN Converges pointwise on (-1, 1].Prove that (fn)nɛN Converges uniformly on Iz for all d > 0, but not on [-1, 1].

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Answered: For n e N, define fn : [-1, 1] → [0, 1]…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.4: Graphs Of Logarithmic Functions

Problem 60SE: Prove the conjecture made in the previous exercise.

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For n e N, define fn : [-1, 1] → [0, 1] by fn(x) = (1 – x2)". For all 8 e (0,1), define Is = [-1, –8] U [8, 1]. (a) Prove that (fn)nEN Converges pointwise on [-1,1]. (b) Provo thet (f nonvomgog uniformly on I for oll & , 0 but not