(ii) Find the pointwise limit of the sequence. (iii) Show that the convergence is uniform on any bounded subset of R.
(ii) Find the pointwise limit of the sequence. (iii) Show that the convergence is uniform on any bounded subset of R.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Number 1...(ii)..(iii)...is real analysis
![EXERCISE 01
of 1
SMTA031
1. Consider a sequence of functions defined on R by
r |_nr
f(x)=
FEBRUARY 2023
(i) Sketch the graphs of fi. 2. f3 and f₁ on the same set of axes.
(ii) Find the pointwise limit of the sequence.
(iii) Show that the convergence is uniform on any bounded subset of R.
2. Show that the series of functions defined by
Σfn(x) = (1 − x) + x(1 − x) + x²(1 − x) + ...
converges pointwise on [0. 1]. Argue that the convergence is not uniform.
3. Find the pointwise limit of the sequence of functions defined on R by the following
and determine whether or not the convergence is uniform.
111 LE TC 0. T](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fdc1e4cee-29b9-4a2d-b096-c551d067f68f%2Fa1706db4-02d2-43fc-8709-e579ab120d83%2Fefusc5v_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXERCISE 01
of 1
SMTA031
1. Consider a sequence of functions defined on R by
r |_nr
f(x)=
FEBRUARY 2023
(i) Sketch the graphs of fi. 2. f3 and f₁ on the same set of axes.
(ii) Find the pointwise limit of the sequence.
(iii) Show that the convergence is uniform on any bounded subset of R.
2. Show that the series of functions defined by
Σfn(x) = (1 − x) + x(1 − x) + x²(1 − x) + ...
converges pointwise on [0. 1]. Argue that the convergence is not uniform.
3. Find the pointwise limit of the sequence of functions defined on R by the following
and determine whether or not the convergence is uniform.
111 LE TC 0. T
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