anonymous
  • anonymous
please help me in solving the eqn. (x e^x)/(e^x - 1) =1 USES SOME OMEGA FUNCTION??????????
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\frac{ xe ^{x} }{e ^{x}-1}=1\]
reemii
  • reemii
taylor:\[ \frac{x(1+x+x^2/2+x^3/6+\dotsb)}{x+x^2/2+x^3/6+\dotsb} = 1\\ %%\iff \frac{(1+x+x^2/2+x^3/6+\dotsb)}{(x+x^2/2+x^3/6+\dotsb)/x} = 1\\ \iff \frac{e^x}{1+x/2+x^2/6 + \dotsb} = 0\\ %\iff \frac{(1+x+x^2/2+x^3/6+\dotsb)}{1+x/2+x^2/6 + \dotsb} = 1\\ %\iff 1+x+x^2/2+x^3/6+\dotsb = 1+x/2+x^2/6 + \dotsb \\ \iff e^x = 1+x/2+x^2/6 + \dotsb =: g(x)\] in my opinion, it can be argued that , when \(x<0\), we have \(e^xg(x)\) when \(x>0\). since \(e^0=g(0)\) this shows that \(x=0\) is the only solution.
reemii
  • reemii
Edit: it's a "1" on the RHS of the second equation. not a "0".

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anonymous
  • anonymous
x=0 IT DOESNT SATISFY THE EQN. AT ALL!!!!!!!!!!!!!!
reemii
  • reemii
x=0. \(e^0=1\) and \(1 +0/2 + 0^2/6 + \dotsb= 1\). I can read small caps better.

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