Question

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

Answer 1

again? :D

Answer 2

watchmath: ur problem has become famous..:D

Answer 3

so this is your problem?

Answer 4

have you done it?

Answer 5

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

Answer 6

i had a dream about this problem last night

Answer 7

:D :D

Answer 8

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

Answer 9

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

Answer 10

pdf*

Answer 11

you are welcome :)

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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.

Answer 16

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

Answer 17

Laplace, are you cantorset?

Answer 18

yes, but dont tell anyone

Answer 19

:D :D

Answer 20

my account has been suspended,

Answer 21

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

Answer 22

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

Answer 23

do you see the pdf file that I attached above?

Answer 24

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

Answer 25

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

Answer 26

oh im going backwards,

Answer 27

this problem has many twists and turns

Answer 28

one sec , im going to read

Answer 29

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.

Answer 30

you can fix it and send me new pdf?

Answer 31

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

Answer 32

hold on

Answer 33

i also want to solve that torus problem,

Answer 34

Here is the updated version:

Answer 35

Are you teaching as a TA laplace?

Answer 36

no, i tutor at the moment online

Answer 37

a TA is what? a teacher assistant?

Answer 38

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

Answer 39

i should,

Answer 40

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

Answer 41

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

Answer 42

thanks

Answer 43

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

Answer 44

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

Answer 45

and how would you upload it, whats a good site

Answer 46

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

Answer 47

where do you want to upload the picture?

Answer 48

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

Answer 49

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

Answer 50

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

Answer 51

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

Answer 52

nope, ln (x-5) in numerator

Answer 53

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

Answer 54

im careful, i use CAS (computer algebra software)

Answer 55

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

Answer 56

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

Answer 57

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

Answer 58

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

Answer 59

hah, yeah

Answer 60

weird to give a student

Answer 61

you changed the left side to log base 3

Answer 62

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

Answer 63

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

Answer 64

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 \(\log_3((x-5))\)

Answer 65

right, i followed the rule

Answer 66

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

Answer 67

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

Answer 68

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

Answer 69

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

Answer 70

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

Answer 71

no

Answer 72

it is equal to ln(ln 3)

Answer 73

oh i think i see it now

Answer 74

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