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#101 Re: Exercises » Series » 2011-08-05 16:12:56
#102 Re: Exercises » Limits! » 2011-08-04 04:47:35
sqrt(-1) doesnt exist because it is indefined.
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*** Edit*** I will stop posting to this subject thread for the foreseeable future.
#103 Re: Exercises » Limits! » 2011-08-04 03:57:48
Yes but check this out! You are forgetting there are also complex answers.
This is one answer for (-1)^(1/3)
Are not the roots of
, ,
#104 Re: Exercises » Limits! » 2011-08-03 16:15:02
Hi;
That is not correct.
No, the odd root of a negative integer is some type of negative real number.
It must be.
#105 Re: Exercises » Limits! » 2011-08-03 06:57:29
How did you calculate that it would approach -1?
They should have been complex numbers, with positive real part.
Notice in the folowing lines how I will use fractions that
necessarily have odd denominators (for odd indices)
Let me show three of my examples worked out:
-------------------------------------------------------------
-------------------------------------------------------------
-------------------------------------------------------------
I will use a fraction relatively much closer to 0:
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#106 Re: Exercises » Limits! » 2011-08-03 02:38:07
and this is 1
Look at all of those negative x-values approaching 0 from the left where x^x is real.
For example, x =
-1/5, -1/25, -1/125, -1/625. -1/3125, ...
For these, x^x is approaching -1.
#107 Re: Help Me ! » "sum of numbers = product of that numbers" problem » 2011-08-03 02:05:33
hi reconsideryouranswer
Where did that line come from?
If c = 3 then b le 1.6666 which would force b to be 1 ??
I think the end of your proof needs a re-think.
Bob
My post has been reedited to show the
correct denominator of (c - 1).
#108 Re: Help Me ! » "sum of numbers = product of that numbers" problem » 2011-08-02 18:16:28
a + b + c = abc
abc - a = b + c
a(bc - 1) = b + c
#109 Re: Exercises » Limits! » 2011-08-02 17:31:53
I am not "forgetting about" ln(1 - x). I was looking right at it and working with it, regardless if I mishandled it. x approaching 0 from either side is not an issue for ln(1 - x), as it is 0. But x approaching 0 from the left side of ln(x) is a problem, just as it is for x approaching from the left of, say, x^x, as those limits do not exist. And where is ln(-x) = ln(x) + ipi coming from? And then, why isn't your alleged expression this
instead of what you typed, because you assumed x --->0-? ---------------------------------------------------------- ------------------------------------------- And -----------------------------------------------------
on using 
#110 Re: Puzzles and Games » points with integer distances » 2011-08-02 11:46:04
In the xy-plane, look at
(0, 8), (-15, 0), (-6, 0), (0, 0), (6, 0), (15, 0), (0, -8)
And look at all of the distances of the 7 C 2 = 21 pairs of these 7 points.
This concept can be extended to greater numbers of Pythagorean triangles
an integer distances using additional points.
#111 Re: Exercises » Limits! » 2011-08-02 10:22:01
16)
The limit needs to approach from the right side of 0,
as amended above. There aren't any real values for
ln(x) from the left side of 0, so it is undefined there.
#112 Re: Puzzles and Games » solve in R » 2011-08-02 07:36:19
solve in R
In solving, I would try to make use of the fact that the sum of the coefficients
of the left-hand side radicands equals the sum of the coefficients of the
right-hand side radicands.
#113 Re: Dark Discussions at Cafe Infinity » """Friends"""" » 2011-07-24 04:56:53
I agree with survival. Friends last aquaintances dont. Differentiate between
the two in your life and might find it more enjoyable to have friends! <3
To me, these are the sets that cover the relationships, with the overlapping
of certain sets:
{strangers}
{acquaintances}
{friends}
{lovers}
{frenemies}
{enemies}
#114 Re: Help Me ! » Multiplying and Dividing Polynomials » 2011-07-18 02:58:46
zee-f, the name of this thread is "Help Me!"
not "Do it for me."
You should always show your own attempts and where
you're stuck.
No posters here should be giving you the answers.
#116 Re: Exercises » Limits! » 2011-07-03 19:56:07
9)
I couldn't come up with another method, can you?
Let x = 1/y. As x --> 0, then 1/y --> 0.
So y --> oo (or -oo).
The limit could be expressed as:
Notes:
--------
Step 2 to step 3 used the Binomial Theorem.
Step 3 through step 5 could use some
justification/details to support the
continued patterns of terms and expressions,
respectively.
#117 Re: Exercises » Limits! » 2011-06-29 04:42:14
7)
Message
Hi gAr,
Nice and well explained solution to Post no. 23.My attempt at 7
Message
Hi 123ronnie321,
That's correct, good job!
Actually, the last line of the solution is wrong, as it violates
the Order of Operations.
It must use grouping symbols, such as
|
#118 Re: Exercises » Limits! » 2011-06-28 19:26:05
2)
Problem:
Let A = (1 + 1/2 + ... + 1/n)
Let B = [1/(n + 1) + 1/(n + 2) + ... + 1/(n + n)]
Let C = A + B
Then B = C - A
#119 Dark Discussions at Cafe Infinity » In part, bowling scores should be based on the number of strikes total » 2011-06-24 15:59:39
- reconsideryouranswer
- Replies: 4
in a game, not as they are now where consecutive strikes have more
weight in the total score, in my opinion.
#120 Re: Puzzles and Games » Some of these solutions to the 8, 8, 3, 3 puzzle do not count: » 2011-06-24 15:51:52
Can't the index for a root only belong to the
set of positive integers?
I am asking this, because in the digit number puzzles, I saw
(The index is shown as .4 as a portion of a solution.)#121 Re: Puzzles and Games » Some of these solutions to the 8, 8, 3, 3 puzzle do not count: » 2011-06-22 07:25:28
new soln for 24 included below, plus numbers to 30 (so far)
11 33 8 8
26 33 8/8;
27 33 8 + 8
28 33 + 8/8
#122 Re: Help Me ! » 1=2 proof » 2011-06-19 06:15:59
Here is another:-
But this proves 2 > 3.
3 < 2
You're missing required grouping symbols, ganesh.
One of the lines above can be fixed by typing:
#123 Re: This is Cool » A new world record! » 2011-06-18 12:13:26
#124 Re: Help Me ! » solve » 2011-06-18 11:43:58
#125 Re: Jai Ganesh's Puzzles » Oral puzzles » 2011-06-17 18:27:11
#1064. What is the sum of the infinite series
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