bishnu

can someone check my solution to the limit as n goes to infinity of n!^(1/n) L=n!^(1/n) Ln(L)=1/nSUM(Ln(n-i),i,0,n-1) use lhoptais rule Ln(L)=Sum(1/(n-i),i,0,n-1) Ln(L)=Sum(1/(1-i/n)*1/n,i,0,n-1) definiton of intergral LnL=int(1/(1-x),0,1) LnL=-Ln(1-x) from 0-1 LnL=Infinity-0 L=infinity

im pretty sure that the reason is that the ancient sumerian civilation counting system had a base 6 system so the number would be equivilant to the number 1000 in our base 10 system.

okay the intergral equals 1/(a^2tan(x)+b) heres how i got it btw i hate latex so just try to follow along okay factor out a cos from the bottom 1/cos^2(atan+b)^2 which equals sec^2/(atan+b)^2 then set u=atan+b so then the intergral becomes 1/au^2 now intergrate and get -1/au then subsitute back in and get -1/(a^2tanx+ba)+c

I have been trying to find the intergral of [math]Int{Sqrt[x^3+1]}[/math]... maybe you guys can help me. First of all im defining an unknown function M(x) this function has the property of M(x)^3+1=1/M'(x)^2 so by subsituting this function in to the intergral i get the intergral to be equal to the inverse of M(x). Now this really doesnt help much because to solve the differntal equation is in essence just solving the intergral unless i some how am able genterate a series solution which i dont think would be possible and it wouldnt be useful either because i would have to take the inverse of that function anyway. So my only option now is to explore the properties of the function M(x). OKay M^-1(x)' is equal to Sqrt(X^3+1)...well that really doesnt help. Damn it what else can i do...i think the best choice would be a series solution now and then invert it...does anyone have any ideas

The problem occurs because you are generalizing the equation to values that are not physically possible. The equation is simply saying that its not possible for the speed to be less than c for a photon.

mathematica spit out -1/2PiEr[sqrt[ln(X)]]+xsqrt[ln[x]] but i have no idea how you would get it...probably write an infinte series for it then intergrate it and try to realte them to some function

In standard ("american" units) the units for force would be pounds, acceleration would be feet per sec^2(this could be converted to mph^2 i you so desire) and the mass would be in slugs(you can ge the weight in slugs by dividing how many pounds it is by gravity's acceleration 32ft/s^2). The best equation you can use is impusle Force*time=change in momentum(momentum is mass times velocity) A much easier approach would be to find the kinetic energy of the cars and find out how much work the magnets have to do agaisnt each other. Magnatism is a weird force. The only difference between the electic force and the magnetic force is that the magnetic force is only generated while moving. Force magnetic=(charge of the particle)(velcotiy)(strength of the magnetic field)(sin(the amount of degrees between the direction of the velocity and magnetic field))) Now i am not sure aboutthis, but i assume that the magneitc field decays at 1/(distance)^2 and i not it will probably give you a decent apporixamtion. OKay the force =(charge)(velocity)(strength of the magnetic field/) since force equals m*a you get(im going to do it symbolic from now on becaus it will take too long with out it)a=(q/m)(v)(Bi/(2x)^2) this is a differental equation(i am assuming that the other car is going the exact same speed and both exert the exact same forc eon each other). Now solving this equation you get(on second thought this equation might not be solvable in any useful way)...oh well mathematica cant solve it so im going to go with scrap the 1/(2x^2) because it makes it non-linear so we can go with that the magneitc field is going to be constant thorugh the "trip" so a=(qB)/m*v which equals v=(Vi)exp{q*B/m*t}, now if we intergrate to get the distance it travels during that time we get x=(Vi*m/qB)(exp{q*b/m*t}-1) now by solving the first equation for time we can then find the distance it travels before it stops(except by using our model it will never stop it will approach zero as it goes toward infinity so you are going to have say that a certain small vaule is going to be zero) and then find the distance it travels. But i think that you would probably want to use the electric force more to get the cars to stop in which case it would be x=K_cQ1*Q2/(m_car)(v)^2 oh BTW vi=velocity intial B=magnetic feild strength q=charge m=mass K_c=columbs constant 8.99E9 i belive i could be wrong t=time

I am a type 1 diabetic and have been one for about a year and a half now. I am able to keep pretty good control of my diabeties and have an average hypoglycimic a1c of about 5.7. Of course, intensive treatment cause many "lows" or hypoglycimic events. The lowest i have ever been is 38 and i have been to 40 about 4-5 times. Now my question is do repeated low blood sugars cause permeant brain damage. I have read that if you have exceeded the age of 8-9 you only have to worry about blood sugars of 1.5mmol/l and less(about 30mg/dl) for a prlonged period of time(but fail to give a quantive defintion of prolonged). Now i have never been that low but i have had repeated blodd sugars of less than 55 and been low enough to lose all of the classic signs hypoglycimia. I'm also curious to the mechanism of "killing" brain cells at low blood sugars o ther than starved for energy.

The scientific method is the foundation of science, but yet now it seems to be placing limitations on the advancement of science. It used to be easy to apply the scientific method. You could easily observe and measure the neccesary interactions and matter you needed for your experment, but as time has progressed it has become harder and harder to do that. That coupled with hesenbergs uncertainty principle and the ever increasing need to observe smaller and smaller things has lead to a state where direct observation of matter and interactions has become in many cases impossible. We must therotically guess a prediction and then test itout and most of the time we must use indirect means to see if it is true. But as string theory is being worked on, it has become obvious that the old scientific method might be unable to prove or disprove its validity. So should we just consider string theory a philisophy because the scientific method cant verify it or should we try to devise a new scientific method which allows for it to be verifed?

Why dont you just try to write down the differental equations for its movement and most likely they will be non linear so just try to solve them using numerical methods and see what you get.

I dont really understand what you are trying to ask. If i understand correctly...the answer is no. The equation does not describe the speed at which the matter must go to convert to energy, but rather the conversion factor between matter and energy. 1/2mV^2 describes the energy an object has while moving,except this value is classical...i dont remember the relavtistic equation

123rock i think you have misunderstood what i am trying to say

What does interpolating mean? But anyway the fractional values diverge similarly to the the integer values of n. My graph does not diverge asytomically. Since each y on the graph repersent s the corresponding convergent value of any a c then at a certain part it just stops(kind of like how arcsin just stops). I think you are a bit confused about my graphing...each x does not correpsond to a n but to the constat c. Can you post pictures on here or do you have to link to them?

what are you trying to prove...its a meaningless assertion to say that 2/0=1/0 okay they are both undefined...you cant have different magnitudes of undefined...but here are someweird things i think about 0/0. It seems it has a differnet value in different ways it is used. look at the function x/x,now for continoutiy reasons you might conclude that 0/0 is 1 for that graph, 0/x for continoutiy you might assume 0/0 is 0 and for x/0 you would assume that it is undefined.

program something to graph the above functions it actually does stay on the line

No that is not what I am trying to say. I'm sorry i must have explained it poorly. [math]x_{n+1}->x^m_n+c[/math](this is the family of functions i am studing)This is a form for an iterated function. Now what i am intrested in is the value this function converges too for each value of c and m...the x doesnt matter at all because it startes at zero but is only there to show how to iterated the function. Now what i did was i set up a graph with the x axis set as a value of c and the y the convergent value as the function is iterated toward infinity. Now each graph would represent 1 value of m. Now what i noticed about these functions was that the values stayed very close to the graph [math]y=x[/math]and then would suddenly start to diverge from the line. As the value om increased the graph stayed more and more on the line, so that leads to my first conjecture that as m goes to infinity the iterated function becomes that graph till it suddenly diverges around .9(ill explain how i got that value later) anotherthing i noticed was the maxium values of all the graphs seemed to lie close to the line [math]y=.7x+.2716..[/math] which if you find where they intersect you get the maxium value. My second conjecture is that all maxium values lie on that line. I am only talking about graphes 1<m.

Okay if time travel to the future is possible free will would not exist. Here is why. Imangine that one of your friends went forward in time one day and there he sees you eating ceral at 10:30 then travels back in time to the time he started from. There he tells you that you will eat ceral at 10:30 tommorrow. Now at 10:29 you have a choice to make eat ceral or not to eat ceral and according to free will you could choose either but since it is already known that you will eat ceral at 10:30 you have to eat it therefore violating your free will. I want to know what people think about this. crap i just noticed i posted this in the wrong forum can a moderate move this oh well

okay i have recently become intrested in iterative functions and im trying to solve the family of equations [math]x_{y+1}->x_y^n+c[/math]...k so using my calculator i graphed the equations i found some compelling results(btw trying to solve algebratically is tedious i belive it would be impossible tofind its limit)the y axes i set as the value the function converges too and x axes a value of c and i set x0 to zero i found that the functions stick to the function y=x and then suddenlystart to diverge from it,but as n increases the graph stay more and moreon y=x so my conjecture is that as n->infinity [math]x_{y+1}->x_y^n+c[/math] becomes the graph y=x through an intervel of about [0,.9]...my second connjecture is that the last convergent value of x_final of any n lies on a solution line of y equals about .7x+.27....

well this is kindof off the topic but i can show you the limits of infinite powers and whyit could help you..sadly its variables cant be solved algebratically, [math]x_(n+1)=x_n^d[/math] [math]x_{final}=x_0^{d^{d^{d^{d^{...}}}}}[/math] you interate to infinty and set you x0 to d you get an infinte amount of powersokay here is how to solve for the values [math]\ln{x_f}=\ln{d}*d^{d^{d^{d^{d^{...}}}}}[/math] no since the number of d's are infinte you can subsitiute the orginal equation in so you get [math]\ln{x_f}=\ln{d}*x_f[/math] [math]d=x_f^{\tfrac{1}{x_f}}[/math] now this cant be solved algebratically but it can be solved using newtons method now lets pretend that that the equation is the inverse of the one above so you plug x_f in instead of d...now use dervatives to find the max value of the function has a max at e and then decreases so hence forth the max value of d=e^(1/e), since the function we just anaylised is the inverse of the function for the value of the power tree we find that the inverse function is a function up to the point e^(1/e) hence the max valule d can be on converge is e^(1/e) where it converges nicely to e. Thats how to solve the power tree i hope that makes sense and will help you a little. Edit sorry about the error in one of my equations it should be fixed now

There might not even be an answer to your question...an explict formula for iteratitive functions is sometimes impossible to create because often time functions of that nature create tons of complexity, especially when there is a buried variable such as a0...in my opinion espcially since the the equation rapidly diverges for most values if not all values of a0 you would be better off using a programmable calculator to rapidly do the iterations for you.

The recent thread e^x=x has gotten me intressted in what it roots are. Through my look at it i think there is a infintude of roots...let me explain one root is very easy to get take the root of x on both sides and you get e=x^1/x which you can easily solve with newtons method setting x0->i but on further anaylsis e^(a+bi)=a+bi a+bi=ln(a+bi) take the polar a+bi=ln((a^2+b^2)^(1/2)cis(arctan(b/a)) set it to exponetial a+bi=ln((a^2+b^2)^(1/2)e^(arctan(b/a)*i)) reduce down and you get a+bi=ln(a^2+b^2)/2+arctan(b/a)*i now because of the periodicness of arctan there should be an infinte # of solutions i belive but i dont know how to solve for them....wait i just relized that there might not be infinity but possibly more than one...does anyone know how to solve.

Well for one, the universe is expanding faster than the speed of light its expanding at the speed of hubbles contast 71 +-4 km/s/Mpc at this moment and in fact evidence suggest that the expansion of the universe is accelerating. Second applying velocity to the speed of time is incoherent. the speedof time equals 3X10^8 meters/second...what would that mean well for one its a self defintion becasue it already has time in it and second it applys distance to the meaning of time...almost meaningless...

i put in the diff forum because im terible at solving diff equations so i was hoping someone would verify the formula i derived in my first post and the meaning of the constants

The acceleration in the equation is constant becuase it is only experencing gravity(im considering the changes in gravity due to height to be trival. I dont understand by what you mean physics doesnt work that way well you offered a solution using vector calaculus instead im just going to right an equation for the forces experenced in the y and the x axis and find the roots on the y and take the time for that and plug it into the x equation

i wish it was that easy but since i have friction in it becomesmuch harder [math]f_{net}=f_{pressure}+f_{friction}[/math] [math]f=pa[/math] [math]f=p_iv_ia/(v_i+ax)[/math] that equals the force from the air cannon using the equation p_iv_i=p_fv_i and since the volume increases by barrel opening(andassuming theprojectile fits snug in the tube) andhow far it has been shotthrough the tube [math]a=p_iv_ia/m(v_i+ax)-kv^2/m[/math] [math]y''=p_iv_ia/m(v_i+ay)-ky'^2/m[/math] but when i solved this diff equation i got obviously wrong equation maybe i just did the math wrong i dont know. i dont even know if that would give the right answer