Problems in Calculus [on hold]
I met difficulties in following two problems. Can I ask for ideas to solve these?
First Problem
For the function $f$ such that $f'$ is continuous in $mathbb{R}$ and $f(0) = 0$, prove or disprove that $int_{0}^{1} |f(x)| dx leq int_{0}^{1} |f'(x)| dx$.
Second Problem
Find all fuctions $f:[0, 1] rightarrow mathbb{R}$, which satisfies following conditions.
$f(0) = f(1) = 0, f(frac{1}{2}) = 1$
$forall x in [0, 1], |f''(x)| leq 8$
calculus
asked yesterday
위승현
4
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put on hold as off-topic by Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad yesterday
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." – Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
I met difficulties in following two problems. Can I ask for ideas to solve these?
First Problem
For the function $f$ such that $f'$ is continuous in $mathbb{R}$ and $f(0) = 0$, prove or disprove that $int_{0}^{1} |f(x)| dx leq int_{0}^{1} |f'(x)| dx$.
Second Problem
Find all fuctions $f:[0, 1] rightarrow mathbb{R}$, which satisfies following conditions.
$f(0) = f(1) = 0, f(frac{1}{2}) = 1$
$forall x in [0, 1], |f''(x)| leq 8$
calculus
asked yesterday
위승현
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad yesterday
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." – Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday
add a comment |
I met difficulties in following two problems. Can I ask for ideas to solve these?
First Problem
For the function $f$ such that $f'$ is continuous in $mathbb{R}$ and $f(0) = 0$, prove or disprove that $int_{0}^{1} |f(x)| dx leq int_{0}^{1} |f'(x)| dx$.
Second Problem
Find all fuctions $f:[0, 1] rightarrow mathbb{R}$, which satisfies following conditions.
$f(0) = f(1) = 0, f(frac{1}{2}) = 1$
$forall x in [0, 1], |f''(x)| leq 8$
calculus
asked yesterday
위승현
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
I met difficulties in following two problems. Can I ask for ideas to solve these?
First Problem
For the function $f$ such that $f'$ is continuous in $mathbb{R}$ and $f(0) = 0$, prove or disprove that $int_{0}^{1} |f(x)| dx leq int_{0}^{1} |f'(x)| dx$.
Second Problem
Find all fuctions $f:[0, 1] rightarrow mathbb{R}$, which satisfies following conditions.
$f(0) = f(1) = 0, f(frac{1}{2}) = 1$
$forall x in [0, 1], |f''(x)| leq 8$
calculus
calculus
asked yesterday
위승현
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
위승현
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
위승현
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
asked yesterday
위승현
4
asked yesterday
위승현
4
4
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
위승현 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
put on hold as off-topic by Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad yesterday
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." – Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
put on hold as off-topic by Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad yesterday
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." – Eevee Trainer, T. Bongers, Kavi Rama Murthy, Nosrati, Saad
If this question can be reworded to fit the rules in the help center, please edit the question.
1
Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday
add a comment |
1
Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday
1
1
Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday
Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday
add a comment |
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Please ask one question at a time. Also, you should include your attempt at a solution to the problem that you are asking about. Where are you stuck? What specific problems are you having?
– Dave
yesterday