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#176 Re: Help Me ! » Maximise ... » 2014-10-19 04:45:24

Hi bobbym.

Someone has asked the same question on another forum – I think you can answer it. smile

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#177 Re: Help Me ! » A question about limits » 2014-10-18 20:49:53

Well, let us assume at each step the original line is broken into fragments of equal length. After the first step we have 4 fragments of length 1/4, after the second we have 16 fragments of length 1/16, etc. Then we have

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Hence

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#183 Re: Help Me ! » Critical points problem: Differential equations » 2014-10-13 22:30:13

I think you mean dy/dt in the second equation. If you divide the second by the first you should get

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eliminating the parameter t.

#185 Re: Help Me ! » Logarithm which goes first? » 2014-10-10 07:57:51

There seems to be some confusion here. What Whizzies means is that (excluding complex numbers) log(y) is only defined for y > 0. The problem involves log(x+3), so y = x+3. It is fine for x = −1; it is the y that needs to be > 0.

#186 Re: Help Me ! » Logarithm which goes first? » 2014-10-10 04:32:43

You’ve got as far as

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Now just solve it for x. smile

#187 Re: Help Me ! » mathematics » 2014-10-09 06:13:05

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#189 Re: Help Me ! » Maximise ... » 2014-10-08 22:07:26

bob bundy wrote:

Why?

It would make no sense for the maximum to be biased towards either x, or y, or z.  So It ought to be when they are equal.

That was what I thought as well until I found this: eek

That might be the maximum but I don’t know how prove it yet (with or without Langrangian multipliers). sad

#190 Re: Dark Discussions at Cafe Infinity » Princeton, Harvard and MIT? » 2014-10-08 05:03:11

bobbym wrote:

I almost got half right.

You did better than over 50% of students from Princeton, Harvard and MIT. lol

#191 Re: Dark Discussions at Cafe Infinity » Princeton, Harvard and MIT? » 2014-10-08 04:26:41

Well, they’re not that difficult. wink


#1. What is CD in Roman numerals?

#2. The cube of a number is that number multiplied by itself three times – true or false?

#3. What is the pseudonym of the writer Mark Twain?

#192 Re: Help Me ! » Sequence Limit Proof » 2014-10-08 04:13:33

You’re welcome. smile

As I said, problems of this kind often demand a lot of ingenuity from the solver, but practice and experience can help a lot. Don’t worry if you can’t come up with such things on the spot – I certainly didn’t for this one! I had to think hard about it for a while. While thinking about it, I realized that the 1 was going to be a problem if I was going to use the triangle inequality, so I tried splitting the 1 into the terms of the sum – and it worked. I mean, it might not have worked and then I would have to start again from the beginning, but fortunately it did. So yeah – practice, practice, practice. cool

#193 Re: Dark Discussions at Cafe Infinity » Princeton, Harvard and MIT? » 2014-10-08 04:04:58

Perhaps those students of Harvard, Princeton and MIT would also be interested in the following questions? wink

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#194 Re: Help Me ! » Sequence Limit Proof » 2014-10-08 01:01:50

If you define N as the minimum of two values, both values must be positive. However for limit problems it’s more usual to define N as the maximum of two values, not minimum.

For problems of this kind you often have to be imaginative. And for this problem I think the key is this:

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Hence:

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Now for r = 1, …, n, we have

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Thus:

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So given
you can take
. cool

#195 Re: Help Me ! » Sequence Limit Proof » 2014-10-07 01:39:00

This step

Maburo wrote:

is not valid. Epsilon might be less than or equal to 2.

I don’t really know how you could go about choosing a suitable N for this problem. Let me think about it. roll

#198 Re: Help Me ! » Discrete Mathematics - Reduction / Deduction! » 2014-10-06 02:16:55

is clearly equivalent to just
.

So we have
,
and
.

and
imply

and
imply

So the given implication is correct.

#199 Re: Help Me ! » Differential equations problem » 2014-10-01 21:25:31

So instead of x' you have to type x^{\prime}?

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#200 Re: Help Me ! » Differential equations problem » 2014-10-01 20:53:21

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Off-topic: Why isn’t LaTeX working? hmm

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