# Is the Limit of the Integral of a Function Equal to its Maximum Value?

• Hunterelite7
In summary, the conversation is discussing a proof for the limit of a certain integral involving a function f(t) as p approaches infinity. The participants suggest using a limiting argument and simplifying the terms by taking the 20th power. The final step involves showing that the function is greater than or equal to the maximum of |f(t)| between [0,1].
Hunterelite7
I am trying to prove that the Limit as p approaches infinity of {integral from 0 to 1[|f(t)|^p dt]}^(1/p) is in fact equal to the max of |f(x)| between [0,1].

Any suggestions I am sure I need to set the limit to less than or equal to and greater than or equal to the max but i don't quite know how

One hint... What is the most contributing term when you take the n th power of each element and sum them up,

keep it simple and start with taking two elements a,b and take the power of 20th...

im sorry I am having a hard time folowing yor terminology is there any way to rephrase

Why is the following true?

$$\left(\int_0^1{|f(t)|^p dt}\right)^{1/p} \leq \left(\int_0^1{\underbrace{(\max{|f(t)|})^p}_{const} dt}\right)^{1/p}=\max|f(t)|\int_0^1{dt}=\max|f(t)|$$
This proof lacks only one limiting argument, can you find it?

ok so how do I show the opposite or that the function is greater than or equal to the max

What function and the max of what?

the function is just vague f(t) and the max is the maximum of |f(t)| between [0,1]

## What is an "Extremely hard concept"?

An "Extremely hard concept" refers to a complex or abstract idea, theory, or principle that is difficult for most people to understand or grasp.

## Why is it important to study "Extremely hard concepts"?

Studying "Extremely hard concepts" can expand our knowledge and understanding of the world around us. It can also improve critical thinking skills and problem-solving abilities.

## What are some examples of "Extremely hard concepts"?

Examples of "Extremely hard concepts" can include advanced mathematics, quantum physics, and theories of relativity. Other examples may include complex philosophical ideas or abstract concepts in computer science.

## How can one effectively learn and understand "Extremely hard concepts"?

Learning and understanding "Extremely hard concepts" requires patience, dedication, and a strong foundation in the subject matter. It can also be helpful to break down the concept into smaller, more manageable parts and seek out additional resources or guidance from experts in the field.

## Why do some people find "Extremely hard concepts" easier to understand than others?

People have different learning styles and backgrounds, which can affect their ability to understand "Extremely hard concepts." Some individuals may have a natural aptitude for certain subjects, while others may struggle more. Ultimately, it is a combination of factors such as intelligence, motivation, and prior knowledge that can impact one's ability to grasp these concepts.

• Calculus and Beyond Homework Help
Replies
23
Views
1K
• Calculus and Beyond Homework Help
Replies
4
Views
908
• Calculus and Beyond Homework Help
Replies
24
Views
2K
• Calculus and Beyond Homework Help
Replies
16
Views
2K
• Calculus and Beyond Homework Help
Replies
3
Views
271
• Calculus and Beyond Homework Help
Replies
7
Views
2K
• Calculus and Beyond Homework Help
Replies
3
Views
1K
• Calculus and Beyond Homework Help
Replies
14
Views
910
• Calculus
Replies
15
Views
2K
• Calculus
Replies
16
Views
2K