Prove $f_n(x) = frac{1}{1+x^n}$ converges uniformly on $(0,1)$
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I am not sure that this correct, please give some feedback and help.
Real analysis: the sequence of functions
Prove $f_n(x) = frac{1}{1+x^n}$ converges uniformly on $(0,1)$
real-analysis analysis
edited Dec 8 '18 at 18:05
Ingix
3,859146
asked Dec 6 '18 at 16:19
nononono
102
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add a comment |
$begingroup$
I am not sure that this correct, please give some feedback and help.
Real analysis: the sequence of functions
Prove $f_n(x) = frac{1}{1+x^n}$ converges uniformly on $(0,1)$
real-analysis analysis
edited Dec 8 '18 at 18:05
Ingix
3,859146
asked Dec 6 '18 at 16:19
nononono
102
$endgroup$
$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
3
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11
add a comment |
$begingroup$
I am not sure that this correct, please give some feedback and help.
Real analysis: the sequence of functions
Prove $f_n(x) = frac{1}{1+x^n}$ converges uniformly on $(0,1)$
real-analysis analysis
edited Dec 8 '18 at 18:05
Ingix
3,859146
asked Dec 6 '18 at 16:19
nononono
102
$endgroup$
I am not sure that this correct, please give some feedback and help.
Real analysis: the sequence of functions
Prove $f_n(x) = frac{1}{1+x^n}$ converges uniformly on $(0,1)$
real-analysis analysis
real-analysis analysis
edited Dec 8 '18 at 18:05
Ingix
3,859146
asked Dec 6 '18 at 16:19
nononono
102
edited Dec 8 '18 at 18:05
Ingix
3,859146
asked Dec 6 '18 at 16:19
nononono
102
edited Dec 8 '18 at 18:05
Ingix
3,859146
edited Dec 8 '18 at 18:05
Ingix
3,859146
edited Dec 8 '18 at 18:05
Ingix
3,859146
3,859146
asked Dec 6 '18 at 16:19
nononono
102
asked Dec 6 '18 at 16:19
nononono
102
asked Dec 6 '18 at 16:19
nononono
102
102
$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
3
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11
add a comment |
$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
3
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11
$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
3
3
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11
add a comment |
1 Answer
1
active
oldest
votes
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Your calculations are correct and prove that $f_n$ does not converge uniformly to the limit $f=1$.
As you can see from the remarks on your question, people vastly prefer that formulas are given with MathJax instead of a photo of hand written notices. This has the advantage that it can be scaled as necessary by any viewer, and is generally very easy to read (your notes are very legible, but that is not true for every contributor). Find a tutorial here, which covers 95% of things I need.
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
$endgroup$
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Your calculations are correct and prove that $f_n$ does not converge uniformly to the limit $f=1$.
As you can see from the remarks on your question, people vastly prefer that formulas are given with MathJax instead of a photo of hand written notices. This has the advantage that it can be scaled as necessary by any viewer, and is generally very easy to read (your notes are very legible, but that is not true for every contributor). Find a tutorial here, which covers 95% of things I need.
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
$endgroup$
add a comment |
$begingroup$
Your calculations are correct and prove that $f_n$ does not converge uniformly to the limit $f=1$.
As you can see from the remarks on your question, people vastly prefer that formulas are given with MathJax instead of a photo of hand written notices. This has the advantage that it can be scaled as necessary by any viewer, and is generally very easy to read (your notes are very legible, but that is not true for every contributor). Find a tutorial here, which covers 95% of things I need.
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
$endgroup$
add a comment |
$begingroup$
Your calculations are correct and prove that $f_n$ does not converge uniformly to the limit $f=1$.
As you can see from the remarks on your question, people vastly prefer that formulas are given with MathJax instead of a photo of hand written notices. This has the advantage that it can be scaled as necessary by any viewer, and is generally very easy to read (your notes are very legible, but that is not true for every contributor). Find a tutorial here, which covers 95% of things I need.
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
$endgroup$
Your calculations are correct and prove that $f_n$ does not converge uniformly to the limit $f=1$.
As you can see from the remarks on your question, people vastly prefer that formulas are given with MathJax instead of a photo of hand written notices. This has the advantage that it can be scaled as necessary by any viewer, and is generally very easy to read (your notes are very legible, but that is not true for every contributor). Find a tutorial here, which covers 95% of things I need.
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
answered Dec 8 '18 at 18:17
IngixIngix
3,859146
3,859146
add a comment |
add a comment |
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$begingroup$
No personal input + Wrong result = ?
$endgroup$
– Did
Dec 6 '18 at 16:20
$begingroup$
Correct result, just in the image.
$endgroup$
– Ingix
Dec 6 '18 at 16:21
3
$begingroup$
Please type it. Don't give us the handwritten proofs.
$endgroup$
– jayant98
Dec 6 '18 at 17:16
$begingroup$
@Ingix Yeah, which is kind of the problem with this question.
$endgroup$
– Did
Dec 8 '18 at 12:01
$begingroup$
Your homework asked you to prove that it is uniformly convergent?
$endgroup$
– zoidberg
Dec 8 '18 at 18:11