Is the following statement correct: If (fn) is a sequence of differentiable functions on [a, b] such that both (fn) and (f%) converge uniformly on [a, b] to ƒ and g respectively, then f is differentiable, and f' = g.} O Yes No Somtimes

Is the following statement correct: If (fn) is a sequence of differentiable functions on [a, b] such that both (fn) and (f%) converge uniformly on [a, b] to ƒ and g respectively, then f is differentiable, and f' = g.} O Yes No Somtimes

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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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

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Is the following statement correct:
If (fn) is a sequence of differentiable functions on [a, b] such that both (fn) and (fn)
converge uniformly on [a, b] to ƒ and g respectively, then
f is differentiable, and f' = g.}
O Yes
O No
Somtimes

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