  # bishnu

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1. 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
2. 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.
3. 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
4. I have been trying to find the intergral of $Int{Sqrt[x^3+1]}$... 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
5. 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.
6. 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
7. 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
8. 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.
9. 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?
10. 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.
11. 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
12. 123rock i think you have misunderstood what i am trying to say
13. 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?
14. 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.
15. program something to graph the above functions it actually does stay on the line
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