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Laters' Maths Help Thread (1 Viewer)

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laters

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Hey guys,

I don't come on here often but I've seen similar threads so I've decided to make one too :) For your reference I am doing MATH1151 this sem.

1) Find . I already know it's 0 but they want a solution using the pinching theorem.
 

InteGrand

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Hey guys,

I don't come on here often but I've seen similar threads so I've decided to make one too :) For your reference I am doing MATH1151 this sem.

1) Find . I already know it's 0 but they want a solution using the pinching theorem.
 

laters

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2) Suppose that for any K>2 the solution to f(x) > K is
 

laters

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Let f be continuous in with

Showthat if there is a number such that then f attains a maximum value in the reals.
[Note the max min theorem applies to finite closed intervals [a,b] only]

Graphically I understand what they're saying... but I am struggling to write a more concrete proof.
 

InteGrand

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Let f be continuous in with

Showthat if there is a number such that then f attains a maximum value in the reals.
[Note the max min theorem applies to finite closed intervals [a,b] only]

Graphically I understand what they're saying... but I am struggling to write a more concrete proof.
If we can assume the extreme value theorem, we can do it as follows.
Let .

By definition of limits to +/- infinity, there exist real numbers such that whenever and whenever . So (because outside this interval, ), and:

(1)

(2) .

By the extreme value theorem (since f is continuous), attains a maximum value on .

Since when , this maximum satisfies . (3)

(1), (2) and (3) imply that f attains a maximum value on (doing so in the interval [N, M]), namely .
 
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Trebla

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This thread will be closed shortly.

After careful consideration, it was decided that user specific threads will no longer be allowed (whether they be one user helping or one user asking for help). We have noticed that the first few threads have spawned multiple others, which is not desirable in the spirit of being an open community. The last thing we want is the Maths forums being full of "User X Maths Help" threads.

You are encouraged to post separate questions in separate threads, though keep in mind a lot of the questions that I have seen so far have been answered before so I suggest to actually do a search first to see if it hasn't been answered already in past threads (which is easier to do when there is a specific thread for a specific question or topic rather than a general user specific thread).
 
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