can it be done??

anywy on a serious note since the equation is tending to going to infinity very fast(from the curve of x^x) we might have a better chance solving say graphically by diffrentiating the equation under integral sign having certain finite limits.(obviously imposing limits on k cos the processing required even in iterrative methods might be too extreme.
 
Differentialtin under a integral sign ??? isnt tht the same thing....
Neways give ur solution so tht everyone understands.

Abt the iterations... if u can guess the closest initial value of "x" depending on "k" then it wont be extreme just like the limits u fix on intergral dependin on "k"
 
hmm maybe i will work it out in spare time. remember seeing this some years back in college prep days. And btw diffrentiation under integral sign is a valid concept. i am not 100% sure it will be used here to get the answer though. But its a try.
 
Grease Monk said:
ok...how does taking log on both sides solve the problem... it just restates it. It might be one of the steps, but def not the soln.
Click to expand...

If we can assume now, that x<1, we can use the expansion for log x, and retain terms upto two or three degrees, which can be solved by regular methods to arrive at the approximate solution.
However, i can't think of anything for x>1
 
I think the soln. is achieved only iteratively as i have given B4, cant be solved by hand u need atleast a calci .
Abt the differentiation inside a an integral...U'll miss the constant there like
diff(x+3)=1
integral(1) = x+constant so it cant be done like this .
 
There is no general way to solve equations of degree 5 or higher. Dont rmr who proved it though :P. This thing can be done using newton raphson. an iterative method that uses.
x[n+1]=x[n]-f(x[n])/f'(x[n])

where x[n] is the nth approximation of the root.

This comes from the first two terms of the taylor's series.
 
That is what I said.
Higher order equations just cannot be solved, except by numerical methods.
Try the books by Chapra, or Numerical Recipes in C (second one is available free on the net, do a google on it; LEGALLY AVAILABLE). They shud give u the answer if indeed it exists.
 
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