7.22 (a) Prove that if {S,(x)} converges uniformly to S(x) on I then {S,(x)} converges point-wise to S(x) on I.(b) Explain why it is impossible for {S,(x)} to converge pointwise to S(x) on I andconverge uniformly to f(x) on I when f(x) = S(x) on I.

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Answered: 7.22 (a) Prove that if {S,(x)}…

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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7.22 (a) Prove that if {S,(x)} converges uniformly to S(x) on I then {S,(x)} converges point- wise to S(x) on I. (b) Explain why it is impossible for {S,(x)} to converge pointwise to S(x) on I and converge uniformly to f(x) on I when f(x) = S(x) on I.