Let (fa). be a sequence of functions f : [0, 1] Rdefined by fa(z) = S2n²z +1 if z %3D Then 1. S.) doesn't converges to 0 pointwisely on (0, 1]. 2. (f) converges to f=0 uniformly on [0, 1] and thus fa(z)dr converges to f(z)dr. 3. (f.) coverges to 0 pointwisely on [0, 1] but not uniformly. 4. (f.) converges to f =0 uniformly on (0, 1] and so (S) converges to 0 uniformly.
Let (fa). be a sequence of functions f : [0, 1] Rdefined by fa(z) = S2n²z +1 if z %3D Then 1. S.) doesn't converges to 0 pointwisely on (0, 1]. 2. (f) converges to f=0 uniformly on [0, 1] and thus fa(z)dr converges to f(z)dr. 3. (f.) coverges to 0 pointwisely on [0, 1] but not uniformly. 4. (f.) converges to f =0 uniformly on (0, 1] and so (S) converges to 0 uniformly.
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
![Let (fa)n be a sequence of functions fa : [0, 1] Rdefined by fa(z)=
2nz +1
, if r<
, if SIS1
Then
1. (f.) doesn't converges to 0 pointwisely on 0, 1].
2 f) coverges to f =0 uniformly on [0, 1] and thus fa(z)dr converges to f(z)dr.
3. (f.) converges to 0 pointwisely on [0, 1] but not uniformly.
4. (f.) converges to f =0 uniformly on 0, 1] and so (S.) converges to 0 uniformly.
The segur nce of functions
on 01 Then on 0. 1
we have
75°F
Farch
TOSHIBA
近
4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Febecefe7-25a8-457a-a711-2bf467d927ae%2Fb5a949ea-71b2-4398-9907-f21992b77829%2F4ock2wi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let (fa)n be a sequence of functions fa : [0, 1] Rdefined by fa(z)=
2nz +1
, if r<
, if SIS1
Then
1. (f.) doesn't converges to 0 pointwisely on 0, 1].
2 f) coverges to f =0 uniformly on [0, 1] and thus fa(z)dr converges to f(z)dr.
3. (f.) converges to 0 pointwisely on [0, 1] but not uniformly.
4. (f.) converges to f =0 uniformly on 0, 1] and so (S.) converges to 0 uniformly.
The segur nce of functions
on 01 Then on 0. 1
we have
75°F
Farch
TOSHIBA
近
4.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
