Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges uniformly on R to a function f. b) Show that f'(x) = limn -->infinity f'n(x), For all x does not = 0, but this equality is false for x = 0. c)What assumption in the theorem on the interchange of the limit and the derivative is missing? I am stuck with that last part (C).

Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1. a) Show that {fn} converges uniformly on R to a function f. b) Show that f'(x) = limn -->infinity f'n(x), For all x does not = 0, but this equality is false for x = 0. c)What assumption in the theorem on the interchange of the limit and the derivative is missing? I am stuck with that last part (C).

Name: Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1.a) Sh
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Description: Let fn: R --> R be defined by : fn(x)= x/(1+nx2), For all n >= 1.a) Show that {fn} converges uniformly on R to a function f.b) Show that f'(x) = limn -->infinity f'n(x), For all x does not = 0, but this equality is false for x = 0.c)What assumption i

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.2: Graphs Of Equations

Problem 78E

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