Limit of a continuous and differentiable function [on hold] The Next CEO of Stack OverflowFinding the limit of a differentiable, continuous functionProve that the derivative of an even differentiable function is odd, and the derivative of an odd is even.Two times differentiable function and limitProve that if $|f(x)| leq x^2$, then the function is continuous and differentiable at $x=0$.Proof that a continuous function is differentiableTwo variables limit / differentiable functionexample of such continuous and differentiable functionProving a Continuous Function Isn't Necessarily DifferentiableProve function is not differentiable even though all directional derivatives exist and it is continuous.Continuous everywhere differentiable nowhere functionDifferentiable and continuous function
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Limit of a continuous and differentiable function [on hold]
The Next CEO of Stack OverflowFinding the limit of a differentiable, continuous functionProve that the derivative of an even differentiable function is odd, and the derivative of an odd is even.Two times differentiable function and limitProve that if $|f(x)| leq x^2$, then the function is continuous and differentiable at $x=0$.Proof that a continuous function is differentiableTwo variables limit / differentiable functionexample of such continuous and differentiable functionProving a Continuous Function Isn't Necessarily DifferentiableProve function is not differentiable even though all directional derivatives exist and it is continuous.Continuous everywhere differentiable nowhere functionDifferentiable and continuous function
$begingroup$
A function f : (a, ∞) → R is differentiable on (a, ∞), and satisfies
$lim_x→∞(f(x) + αf(x))$ = $0$,
where α is a positive constant.
Prove that $lim_x→∞f(x)$ = $0$.
limits derivatives continuity
asked Mar 28 at 9:31
dodo bcdodo bc
1
$endgroup$
put on hold as off-topic by Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu Mar 28 at 12:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu
add a comment |
$begingroup$
A function f : (a, ∞) → R is differentiable on (a, ∞), and satisfies
$lim_x→∞(f(x) + αf(x))$ = $0$,
where α is a positive constant.
Prove that $lim_x→∞f(x)$ = $0$.
limits derivatives continuity
asked Mar 28 at 9:31
dodo bcdodo bc
1
$endgroup$
put on hold as off-topic by Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu Mar 28 at 12:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu
1
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
1
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
1
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36
add a comment |
$begingroup$
A function f : (a, ∞) → R is differentiable on (a, ∞), and satisfies
$lim_x→∞(f(x) + αf(x))$ = $0$,
where α is a positive constant.
Prove that $lim_x→∞f(x)$ = $0$.
limits derivatives continuity
asked Mar 28 at 9:31
dodo bcdodo bc
1
$endgroup$
A function f : (a, ∞) → R is differentiable on (a, ∞), and satisfies
$lim_x→∞(f(x) + αf(x))$ = $0$,
where α is a positive constant.
Prove that $lim_x→∞f(x)$ = $0$.
limits derivatives continuity
limits derivatives continuity
asked Mar 28 at 9:31
dodo bcdodo bc
1
asked Mar 28 at 9:31
dodo bcdodo bc
1
asked Mar 28 at 9:31
dodo bcdodo bc
1
asked Mar 28 at 9:31
dodo bcdodo bc
1
asked Mar 28 at 9:31
dodo bcdodo bc
1
1
put on hold as off-topic by Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu Mar 28 at 12:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu
put on hold as off-topic by Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu Mar 28 at 12:30
This question appears to be off-topic. The users who voted to close gave this specific reason:
- "This question is missing context or other details: Please provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Michael Rybkin, 5xum, Rebellos, Delta-u, Tianlalu
1
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
1
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
1
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36
add a comment |
1
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
1
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
1
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36
1
1
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
1
1
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
1
1
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Hint : Write $$f(x) = fracf(x)+alpha f(x)1+alpha.$$
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
$endgroup$
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Hint : Write $$f(x) = fracf(x)+alpha f(x)1+alpha.$$
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
$endgroup$
add a comment |
$begingroup$
Hint : Write $$f(x) = fracf(x)+alpha f(x)1+alpha.$$
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
$endgroup$
add a comment |
$begingroup$
Hint : Write $$f(x) = fracf(x)+alpha f(x)1+alpha.$$
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
$endgroup$
Hint : Write $$f(x) = fracf(x)+alpha f(x)1+alpha.$$
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
answered Mar 28 at 9:55
TheSilverDoeTheSilverDoe
4,997215
4,997215
add a comment |
add a comment |
1
$begingroup$
Hi and welcome to the site! Since this is a site that encourages and helps with learning, it is best if you show your own ideas and efforts in solving the question. Can you edit your question to add your thoughts and ideas about it? Don't worry if it's wrong - that's what we're here for.
$endgroup$
– 5xum
Mar 28 at 9:35
1
$begingroup$
Do you really mean $f(x)+ alpha f(x)$ ?
$endgroup$
– Fred
Mar 28 at 9:36
1
$begingroup$
Also, don't get discouraged by the downvote. I downvoted the question and voted to close it because at the moment, it is not up to site standards (you have shown no work you did on your own). If you edit your question so that you show what you tried and how far you got, I will not only remove the downvote, I will add an upvote.
$endgroup$
– 5xum
Mar 28 at 9:36