How would I go about solving this type of question [on hold]

-1

Find integers l,m,n and p such that :

$$frac{l}{m} le int_a^b mathit f(x) le frac np $$

asked 2 days ago

Unknown variable

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put on hold as off-topic by Frpzzd, amWhy, Shailesh, mrtaurho, KReiser 2 days ago

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." – amWhy, mrtaurho

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What information about $f$, $a$ and $b$ is known?
– Ángel Mario Gallegos
2 days ago

f is a continuous function and a and b are real numbers.
– Unknown variable
2 days ago

add a comment |

-1

Find integers l,m,n and p such that :

$$frac{l}{m} le int_a^b mathit f(x) le frac np $$

asked 2 days ago

Unknown variable

New contributor

put on hold as off-topic by Frpzzd, amWhy, Shailesh, mrtaurho, KReiser 2 days ago

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." – amWhy, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

What information about $f$, $a$ and $b$ is known?
– Ángel Mario Gallegos
2 days ago

f is a continuous function and a and b are real numbers.
– Unknown variable
2 days ago

add a comment |

-1

Find integers l,m,n and p such that :

$$frac{l}{m} le int_a^b mathit f(x) le frac np $$

asked 2 days ago

Unknown variable

New contributor

Find integers l,m,n and p such that :

$$frac{l}{m} le int_a^b mathit f(x) le frac np $$

real-analysis

asked 2 days ago

Unknown variable

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asked 2 days ago

Unknown variable

New contributor

asked 2 days ago

Unknown variable

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asked 2 days ago

Unknown variable

asked 2 days ago

Unknown variable

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put on hold as off-topic by Frpzzd, amWhy, Shailesh, mrtaurho, KReiser 2 days ago

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." – amWhy, mrtaurho

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 Frpzzd, amWhy, Shailesh, mrtaurho, KReiser 2 days ago

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." – amWhy, mrtaurho

If this question can be reworded to fit the rules in the help center, please edit the question.

What information about $f$, $a$ and $b$ is known?
– Ángel Mario Gallegos
2 days ago

f is a continuous function and a and b are real numbers.
– Unknown variable
2 days ago

add a comment |

What information about $f$, $a$ and $b$ is known?
– Ángel Mario Gallegos
2 days ago

f is a continuous function and a and b are real numbers.
– Unknown variable
2 days ago

What information about $f$, $a$ and $b$ is known?
– Ángel Mario Gallegos
2 days ago

f is a continuous function and a and b are real numbers.
– Unknown variable
2 days ago

add a comment |

1 Answer
1

active

oldest

votes

If $f(x)$ is continuous, it achieves its maximum and minimum in any closed interval.

$$|b-a|f_{min}leint_a^bf(x)dxle|b-a|f_{max}$$

Take $l=lfloor|b-a|f_{min}rfloor,m=1=p,n=lceil|b-a|f_{max}rceil$.

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

add a comment |

1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

If $f(x)$ is continuous, it achieves its maximum and minimum in any closed interval.

$$|b-a|f_{min}leint_a^bf(x)dxle|b-a|f_{max}$$

Take $l=lfloor|b-a|f_{min}rfloor,m=1=p,n=lceil|b-a|f_{max}rceil$.

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

add a comment |

If $f(x)$ is continuous, it achieves its maximum and minimum in any closed interval.

$$|b-a|f_{min}leint_a^bf(x)dxle|b-a|f_{max}$$

Take $l=lfloor|b-a|f_{min}rfloor,m=1=p,n=lceil|b-a|f_{max}rceil$.

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

add a comment |

If $f(x)$ is continuous, it achieves its maximum and minimum in any closed interval.

$$|b-a|f_{min}leint_a^bf(x)dxle|b-a|f_{max}$$

Take $l=lfloor|b-a|f_{min}rfloor,m=1=p,n=lceil|b-a|f_{max}rceil$.

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

If $f(x)$ is continuous, it achieves its maximum and minimum in any closed interval.

$$|b-a|f_{min}leint_a^bf(x)dxle|b-a|f_{max}$$

Take $l=lfloor|b-a|f_{min}rfloor,m=1=p,n=lceil|b-a|f_{max}rceil$.

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

edited 2 days ago

answered 2 days ago

Shubham Johri

4,459717

answered 2 days ago

Shubham Johri

4,459717

answered 2 days ago

Shubham Johri

4,459717

add a comment |

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