myininaya
  • myininaya
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
Mathematics
chestercat
  • chestercat
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watchmath
  • watchmath
again? :D
anonymous
  • anonymous
watchmath: ur problem has become famous..:D
myininaya
  • myininaya
1 Attachment

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myininaya
  • myininaya
so this is your problem?
myininaya
  • myininaya
have you done it?
watchmath
  • 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.
myininaya
  • myininaya
i had a dream about this problem last night
watchmath
  • watchmath
:D :D
myininaya
  • myininaya
i feel like i really dont sleep when i dream about math problems
myininaya
  • myininaya
i have to look at this later but im very interested thanks for the link
myininaya
  • myininaya
pdf*
watchmath
  • watchmath
you are welcome :)
anonymous
  • anonymous
i got as far as g = C e^ int ( f' / ( f' - f)
anonymous
  • anonymous
i think, why did someone say , let F = e ^f, and G = e^g
anonymous
  • anonymous
then ln F = f , and ln G = f ,
watchmath
  • 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
  • watchmath
I mean after you find \(g=Ce^{\int f'/(f'-f)}\)
watchmath
  • watchmath
Laplace, are you cantorset?
anonymous
  • anonymous
yes, but dont tell anyone
watchmath
  • watchmath
:D :D
anonymous
  • anonymous
my account has been suspended,
anonymous
  • anonymous
im here to do math, not to debate with admin :)
anonymous
  • anonymous
so from that g , whats g ' , its ...
watchmath
  • watchmath
do you see the pdf file that I attached above?
anonymous
  • anonymous
g ' = f' ( f' - f) C e ^ ( int f' / f' - f ) ?
watchmath
  • watchmath
correct, which is f'g/(f'-f)
anonymous
  • anonymous
oh im going backwards,
anonymous
  • anonymous
this problem has many twists and turns
anonymous
  • anonymous
one sec , im going to read
watchmath
  • 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
  • anonymous
you can fix it and send me new pdf?
anonymous
  • anonymous
or you already updated? i dont know how to write pdf's, thats pretty cool
watchmath
  • watchmath
hold on
anonymous
  • anonymous
i also want to solve that torus problem,
watchmath
  • watchmath
Here is the updated version:
watchmath
  • watchmath
Are you teaching as a TA laplace?
anonymous
  • anonymous
no, i tutor at the moment online
anonymous
  • anonymous
a TA is what? a teacher assistant?
watchmath
  • watchmath
Yes, usually if you take a graduate program in math you are a TA as well.
anonymous
  • anonymous
i should,
anonymous
  • 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
  • watchmath
If you have an interesting problem please post it here: http://www.ask.watchmath.com
anonymous
  • anonymous
thanks
anonymous
  • anonymous
whats an easy way to draw a graph and upload it? microsoft paint?
watchmath
  • 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
  • anonymous
and how would you upload it, whats a good site
anonymous
  • anonymous
i use sendspace.com, not sure how long they keep it up
watchmath
  • watchmath
where do you want to upload the picture?
anonymous
  • anonymous
well i can draw problems and solve them, and you can look over
anonymous
  • anonymous
www.sendspace.com , is a website that you can upload anything
anonymous
  • 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
  • watchmath
so the left hand side is \(\frac{2}{\ln 3\ln(x-5)}\)
anonymous
  • anonymous
nope, ln (x-5) in numerator
anonymous
  • anonymous
i know, its ambiguous when you have a bad student :)
anonymous
  • anonymous
im careful, i use CAS (computer algebra software)
anonymous
  • anonymous
maple, did you know that maple cant find tan (105 degrees) ,
anonymous
  • anonymous
tan ( 105* Pi/180) , its an exact angle, i want to complain to the makers
watchmath
  • 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
  • watchmath
sorry ..... It should be 4x^2=25 So x=5/2 then no solution as well
anonymous
  • anonymous
hah, yeah
anonymous
  • anonymous
weird to give a student
anonymous
  • anonymous
you changed the left side to log base 3
anonymous
  • anonymous
2/ln 3 * ln ( x - 5) = log base 3 ( x-2) + log base 3 (5x) , what happened to your left side?
anonymous
  • anonymous
your left side is log _3 (x-5) / log _3 ln 3 * 2/ln 3
watchmath
  • 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
  • anonymous
right, i followed the rule
anonymous
  • anonymous
but you have 2/ln 3 *log _3 (x-5) / log _3 (ln 3)
anonymous
  • anonymous
and whats log _3 of ln 3 ? log base 3 of ln 3
watchmath
  • watchmath
In that case I thin we can't simplify it nicely.
anonymous
  • 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
  • anonymous
so it must be the case that ln 3 * log_3 ln 3 = 1 ?
watchmath
  • watchmath
no
watchmath
  • watchmath
it is equal to ln(ln 3)
anonymous
  • anonymous
oh i think i see it now
anonymous
  • 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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