Let (fi)N be a sequence of differentiable functions from I to R. For each n e N, prove that the function ƒ = f, is differentiable on I i=1 and f'(c) = Ef(c) for all c E I. i=1

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.2: Exponential Functions
Problem 58E
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Let (fi)N be a sequence of differentiable functions from I to R. For
each n e N, prove that the function ƒ = f, is differentiable on I
i=1
and f'(c) = Ef(c) for all c E I.
i=1
Transcribed Image Text:Let (fi)N be a sequence of differentiable functions from I to R. For each n e N, prove that the function ƒ = f, is differentiable on I i=1 and f'(c) = Ef(c) for all c E I. i=1
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