Exercise 5.4.1. Sketch a graph of (1/2)h(2x) on [−2,3]. Give a qualitative description of the functions hn(x) = ——h(2 -h(2x) as n gets larger. Now, define ∞ ∞ 1 g(x) = hn(x) = = 2n Σ 2, h(22). n=0 n=0 The claim is that g(x) is continuous on all of R but fails to be differentiable at any point.
Exercise 5.4.1. Sketch a graph of (1/2)h(2x) on [−2,3]. Give a qualitative description of the functions hn(x) = ——h(2 -h(2x) as n gets larger. Now, define ∞ ∞ 1 g(x) = hn(x) = = 2n Σ 2, h(22). n=0 n=0 The claim is that g(x) is continuous on all of R but fails to be differentiable at any point.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Exercise 5.4.1. Sketch a graph of (1/2)h(2x) on [−2,3]. Give a qualitative
description of the functions
hn(x) = ——h(2
-h(2x)
as n gets larger.
Now, define
∞
∞
1
g(x) = hn(x) =
=
2n
Σ 2, h(22).
n=0
n=0
The claim is that g(x) is continuous on all of R but fails to be differentiable at
any point.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcfc00cc1-fefc-469e-8067-6e606b69cdb3%2F42345fcf-52f8-4c90-ac92-09f7848c744b%2Fx0emucv_processed.png&w=3840&q=75)
Transcribed Image Text:Exercise 5.4.1. Sketch a graph of (1/2)h(2x) on [−2,3]. Give a qualitative
description of the functions
hn(x) = ——h(2
-h(2x)
as n gets larger.
Now, define
∞
∞
1
g(x) = hn(x) =
=
2n
Σ 2, h(22).
n=0
n=0
The claim is that g(x) is continuous on all of R but fails to be differentiable at
any point.
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