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September 20, 2025, 08:28:57 am
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Author Topic: MAX?  (Read 4607 times)  Share 

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m@tty

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MAX?
« on: August 16, 2009, 06:41:05 pm »
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Quick question.
If the range of a funtion is then what is the maximum.
What is it stated as? since it never actually reaches 1, if I've been taught this I have completely forgotten.

Thanks
« Last Edit: August 16, 2009, 06:43:42 pm by m@tty »
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dekoyl

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Re: MAX?
« Reply #1 on: August 16, 2009, 06:46:45 pm »
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What is the function? If it's an exponential graph, there is no maximum stationary point. (so asymptote at )
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/0

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Re: MAX?
« Reply #2 on: August 16, 2009, 07:48:24 pm »
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I think he means for example defined in . What is the maximum?
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m@tty

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Re: MAX?
« Reply #3 on: August 16, 2009, 10:01:32 pm »
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Yeah thats what I mean.
Because the function is never equal to 1.

If the question asked what is the max value of

Would the answer be in the form of a limit?
My guess is:

Is this the correct answer??
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kamil9876

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Re: MAX?
« Reply #4 on: August 17, 2009, 09:49:09 am »
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Quote from: m@tty on August 16, 2009, 10:01:32 pm
Yeah thats what I mean.
Because the function is never equal to 1.

If the question asked what is the max value of

Would the answer be in the form of a limit?
My guess is:

Is this the correct answer??

Technically speaking, in your example it would be:



because it's what you approach comming from the negative side.

If however your domain was, just for example R/{1}, then both:

and

would be correct and so would be correct. (in order for THE LIMIT to exist, limits from both sides must by definition).

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zzdfa

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Re: MAX?
« Reply #5 on: August 17, 2009, 10:09:43 am »
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sorry but isnt all that stuff a bit irrelevant?
it's asking for a maximum value, and you're answering with a limit.

personally i would write, there is no maximum value because for each x in (-inf,1) there is another p, 1>p>x


where did you see this question? it looks like some sloppy trial exam question.
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/0

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Re: MAX?
« Reply #6 on: August 17, 2009, 12:08:03 pm »
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If it asks for the maximum value then couldn't you just say 1, since , so even though x = 1 is not defined, we know that x = 0.9999... is defined.
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m@tty

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Re: MAX?
« Reply #7 on: August 17, 2009, 04:28:34 pm »
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Quote from: zzdfa on August 17, 2009, 10:09:43 am
sorry but isnt all that stuff a bit irrelevant?
it's asking for a maximum value, and you're answering with a limit.

personally i would write, there is no maximum value because for each x in (-inf,1) there is another p, 1>p>x


where did you see this question? it looks like some sloppy trial exam question.
It's not a question from any exam.
Just some concept I was unsure of.
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kamil9876

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Re: MAX?
« Reply #8 on: August 17, 2009, 06:00:47 pm »
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Quote from: /0 on August 17, 2009, 12:08:03 pm
If it asks for the maximum value then couldn't you just say 1, since , so even though x = 1 is not defined, we know that x = 0.9999... is defined.

But is it part of the range? :P  I think it's like saying 0.99999...<1 AND 0.9999...=1.

Remember a number is determind by it's value, not the decimal representation, ie 0.999... is a shorthand way of talking about a sum of a geometric sequence whose value is 1 so you havn't avoided talking about 1. IMO

@zzdfa: I think you're right, I guess I focused too much on limit and not enough on the initial question :P
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m@tty

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Re: MAX?
« Reply #9 on: August 17, 2009, 07:42:28 pm »
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Is this the answer?
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TrueTears

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Re: MAX?
« Reply #10 on: August 17, 2009, 07:48:41 pm »
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No, there is no maximum value.
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dcc

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Re: MAX?
« Reply #11 on: August 17, 2009, 07:52:08 pm »
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In this case, the function attains no maximum value on the interval provided.  

If we define , the best we can say is that the .

http://en.wikipedia.org/wiki/Supremum#Greatest_elements
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m@tty

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Re: MAX?
« Reply #12 on: August 17, 2009, 08:09:30 pm »
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So this is not required for methods?
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TrueTears

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Re: MAX?
« Reply #13 on: August 17, 2009, 08:25:49 pm »
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Correct.
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m@tty

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Re: MAX?
« Reply #14 on: August 17, 2009, 08:28:58 pm »
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Wait.
What is the actual definition of a max?
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