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#4 Re: Exercises » Integration by Substitution » 2020-05-16 12:07:35

Zhylliolom wrote:


I wasn't able to solve this using substitution, but here's a solution I came up with:

#5 Re: Exercises » ..find X » 2020-05-16 07:27:38

Ahhh, I see it now! Thanks, Bob! smile

#10 Re: Ganesh's Puzzles » Mensuration » 2018-10-08 10:41:16

ganesh wrote:


M # 444. Two right circular cylinders of equal volume have their heights in the ratio 1:2. Find the ratio of their radii.

Hi ganesh,

#11 Re: Ganesh's Puzzles » Oral puzzles » 2018-10-08 10:37:18

ganesh wrote:



#4242. If the numerator of a fraction is increased by 300% and the denominator is increased by 500%, the resultant fraction is

. What was the original fraction?

#12 Re: Help Me ! » A pool table » 2017-05-02 14:42:21

Assuming the last time the ball hits an edge counts for the 6 total, I get a 2:1 ratio for the lengths of the sides. Otherwise, I don't think it's possible.


#13 Re: Euler Avenue » Transcendental Numbers » 2017-05-02 14:27:03

zetafunc wrote:
ganesh wrote:

Whats so special about the TN
1.444667861..................?????? big_smile

Is it known if this number (i.e. e^(1/e)) is transcendental?

It has not been proven to be transcendental, I don't think.

#14 Re: Dark Discussions at Cafe Infinity » Some Great Youtube Channels to visit » 2017-05-02 14:11:07

Some channels I really enjoy that were not mentioned here already:

3Blue1Brown - Explains a wide variety of maths topics in a very clear way.
CGP Grey - Amazingly researched videos covering a wide arrange of topics, including geography, politics, philosophy, technology, etc.
Jacksflims - Comedy sketches and several series of comedy videos (Yesterday I Asked You, Your Grammar drags, etc.)
Bad Lip Reading - Incredibly funny bad lip reading of scenes from movies, TV shows and even the debates from the last presidential elections.
Vi Hart - I'm sure you've heard of this one before. A fun channel on recreational maths and music.
Real Life Lore - Mostly geography and history, but in a really interesting way, with a bunch videos asking the question of what would it be like if great empires of history existed today.

#15 Re: Help Me ! » I can't find the third answer in the polar equations. » 2017-03-09 12:28:34

Good to know! x)

Yeah, I've been a been lacking in the uni department lately, because I got a temporary job, so I had less time to study, but it's pretty good otherwise! big_smile

#18 Re: Help Me ! » I can't find the third answer in the polar equations. » 2017-03-08 08:00:39

Actually, there is another solution, since in polar coordinates the point
is the same one as the point

So, another equation that would give you a solution would be

#19 Re: Computer Math » 2-dimensional integral involving Bessel functions » 2016-11-02 20:31:44

bobbym wrote:

The double integral you posted in post #9,

that one does not converge.

There shouldn't minuses in those exponents.

#20 Re: Help Me ! » Parenthensis » 2016-09-01 16:06:22


Well, one sure way to get a definitive result is to go through all the possibilities, which are not many, since you just have to choose which operation gets performed before which. 4 operations means there are 4!=24 different orders to do the operations in. So, for example, you could label each operation with a number 1 through 4, then list out all the permutations of the sequence 1,2,3,4 and perform the operations in the order signified by each permutation. E.g., 3241 would mean you'd group them like 5-((2*(6-4))+2).

#21 Re: Help Me ! » Set problem of proving equation. » 2016-06-21 01:22:43

Hi Bob,

You can superscript the "\prime" to have it look like normal, like so:

#22 Re: This is Cool » On Infinity » 2016-06-20 08:51:39

Besides, the notion of 0.999... doesn't even make sense, i.e., it is not a valid decimal representation.

#23 Re: Computer Math » Polynomial Root Finding » 2016-06-20 08:42:18

Hmm, out Intro to NA professor mentioned that trick with the example of the integral

It's quite brilliant.

Also, yes, if you ran it to a[0], you would get an approximation of ln(9/8). This is also, I think, the only value of a[0] for which the sequence a[n] converges.

#24 Re: Computer Math » Polynomial Root Finding » 2016-06-16 15:55:11

bobbym wrote:

Here I suggest you use your own head.

f[x_] := x^6 + x^5 - 5 x^4 - 4 x^3 + 6 x^2 + 3 x - 1

x =0.

x = x - f[x]/f'[x]

Well, of course, Newton's method has a number of conditions to be met so that it would converge.

Also, isolating the zeroes might not be a bad idea.

#25 Re: Computer Math » Polynomial Root Finding » 2016-06-16 15:41:49

Agnishom wrote:

Something like this?

I do not understand. The NewtonRaphson function does not take f as an argument in his code.

It uses f as a global variable, assigned a value outside of the subroutine, so, to call it for a function, you'd have to set f to that function before calling NewtonRaphson. I assume it works without much problem, but that is a silly thing to do...

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