calculus dream problem?
(fg)'=f'g' and (fg)''=f''g''
I don't think this what you guys are looking for but here what i did

- myininaya

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- watchmath

again? :D

- anonymous

watchmath: ur problem has become famous..:D

- myininaya

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## More answers

- myininaya

so this is your problem?

- myininaya

have you done it?

- watchmath

Check it here.
It is solution for f. The g will be of the same form, but then the coefficients need to be adjusted.

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- myininaya

i had a dream about this problem last night

- watchmath

:D :D

- myininaya

i feel like i really dont sleep when i dream about math problems

- myininaya

i have to look at this later but im very interested
thanks for the link

- myininaya

pdf*

- watchmath

you are welcome :)

- anonymous

i got as far as g = C e^ int ( f' / ( f' - f)

- anonymous

i think, why did someone say , let F = e ^f, and G = e^g

- anonymous

then ln F = f , and ln G = f ,

- watchmath

Yes, that's good laplace. Then basically the idea is that from that g we can express, g' and g'' in terms of g. By doing that, then we have an equation in terms of f,f' and f'' only.

- watchmath

I mean after you find
\(g=Ce^{\int f'/(f'-f)}\)

- watchmath

Laplace, are you cantorset?

- anonymous

yes, but dont tell anyone

- watchmath

:D :D

- anonymous

my account has been suspended,

- anonymous

im here to do math, not to debate with admin :)

- anonymous

so from that g , whats g ' , its ...

- watchmath

do you see the pdf file that I attached above?

- anonymous

g ' = f' ( f' - f) C e ^ ( int f' / f' - f ) ?

- watchmath

correct, which is f'g/(f'-f)

- anonymous

oh im going backwards,

- anonymous

this problem has many twists and turns

- anonymous

one sec , im going to read

- watchmath

there is some little mistake whenn I said that if f'=f then f'g=0 it should be then fg'=0. But similar to what I wrote we will arrive a t contradiction.

- anonymous

you can fix it and send me new pdf?

- anonymous

or you already updated?
i dont know how to write pdf's, thats pretty cool

- watchmath

hold on

- anonymous

i also want to solve that torus problem,

- watchmath

Here is the updated version:

##### 1 Attachment

- watchmath

Are you teaching as a TA laplace?

- anonymous

no, i tutor at the moment online

- anonymous

a TA is what? a teacher assistant?

- watchmath

Yes, usually if you take a graduate program in math you are a TA as well.

- anonymous

i should,

- anonymous

sorry was away, i enjoy math. but sometimes i cant remember the last problem i was working on.
some people say its ok to forget all the loose ends problems, and start fresh. dunno. i have various interests in math, linear algebra, diff eq.
they always end up in an interesting problem

- watchmath

If you have an interesting problem please post it here:
http://www.ask.watchmath.com

- anonymous

thanks

- anonymous

whats an easy way to draw a graph and upload it? microsoft paint?

- watchmath

is it a graph of a well defined function? if it is you can plot it at http://fooplot.com and save it as an image

- anonymous

and how would you upload it, whats a good site

- anonymous

i use sendspace.com, not sure how long they keep it up

- watchmath

where do you want to upload the picture?

- anonymous

well i can draw problems and solve them, and you can look over

- anonymous

www.sendspace.com , is a website that you can upload anything

- anonymous

ok heres a question i was working on,
i got no solution
2/ln 3 * ln ( x - 5) = log base 3 ( x-2) + log base 3 (5x) ,
i made the right side a product and then changed base

- watchmath

so the left hand side is
\(\frac{2}{\ln 3\ln(x-5)}\)

- anonymous

nope, ln (x-5) in numerator

- anonymous

i know, its ambiguous when you have a bad student :)

- anonymous

im careful, i use CAS (computer algebra software)

- anonymous

maple, did you know that maple cant find tan (105 degrees) ,

- anonymous

tan ( 105* Pi/180) , its an exact angle, i want to complain to the makers

- watchmath

Oh ok, then by the change of base formula we have
\(2\log_3(x-5)=\log_3((x-2)(5x))\)
So
\((x-5)^2=(x-2)(5x)\)
\(x^2-10x+255=5x^2-10x\)
\(4x^2=225\)
\(x=\pm\frac{15}{2}\)
only the postive one works

- watchmath

sorry .....
It should be 4x^2=25
So x=5/2 then no solution as well

- anonymous

hah, yeah

- anonymous

weird to give a student

- anonymous

you changed the left side to log base 3

- anonymous

2/ln 3 * ln ( x - 5) = log base 3 ( x-2) + log base 3 (5x) ,
what happened to your left side?

- anonymous

your left side is log _3 (x-5) / log _3 ln 3 * 2/ln 3

- watchmath

remember that
\[\log_ba=\frac{\log_c a}{\log_cb}\]
Where you can choose your c as you like. Choosince c to be the natural number e, then the left side is exactly \(\log_3((x-5))\)

- anonymous

right, i followed the rule

- anonymous

but you have
2/ln 3 *log _3 (x-5) / log _3 (ln 3)

- anonymous

and whats log _3 of ln 3 ? log base 3 of ln 3

- watchmath

In that case I thin we can't simplify it nicely.

- anonymous

its funny you did that and still got right answer. my instinct would be to change the right side to ln instead of log base 3

- anonymous

so it must be the case that ln 3 * log_3 ln 3 = 1 ?

- watchmath

no

- watchmath

it is equal to ln(ln 3)

- anonymous

oh i think i see it now

- anonymous

for the left side we have
2/( ln 3) * ln (x-5)
= 2/ln 3 * log_3 (x-5) / log _3 (e)
= 2 *log_3 (x-5) * 1/ ( ln 3 * log _3 (e)
= log _3 (x-5)^2 * 1/ ( log _3 e^(ln 3) )
= log _3 (x-5)^2* 1 / ( log _3 3 )
= log_3 (x-5)^2 * 1

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