tions gn [0, 1] → R given by : Consider the sequence of func- In (x)= = lim gn- (a) Show that (gn) converges uniformly on [0, 1] and find g Show that g is differentiable and compute g'(x) for all r = [0, 1]. (b) Show that (gn) converges pointwise on [0, 1]. Is the convergence uni- form? Let h= lim gn, and compare h and g'. Are they the same? n

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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tions gn [0, 1] → R given by
In(x) =
x"
n
Consider the sequence of func-
(a) Show that (gn) converges uniformly on [0, 1] and find g = lim gn.
Show that g is differentiable and compute g'(x) for all r = [0, 1].
(b) Show that (gn) converges pointwise on [0, 1]. Is the convergence uni-
form? Let h= lim gn, and compare h and g'. Are they the same?
Transcribed Image Text:tions gn [0, 1] → R given by In(x) = x" n Consider the sequence of func- (a) Show that (gn) converges uniformly on [0, 1] and find g = lim gn. Show that g is differentiable and compute g'(x) for all r = [0, 1]. (b) Show that (gn) converges pointwise on [0, 1]. Is the convergence uni- form? Let h= lim gn, and compare h and g'. Are they the same?
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