anonymous
  • anonymous
Use the intermediate value theorem to show that the equation e^(-x)=x has at least one real solution.
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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asnaseer
  • asnaseer
@j814wong - do you know what the intermediate value theorem states?
anonymous
  • anonymous
Sorry for the late reply. Yes. If f is continuous on a closed interval [a,b] and k is any number between f(a) and f(b), inclusive, then there is at least one number x in the interval [a,b] such that f(x)=k That's the formal definition as opposed to the one I'd give on teh spot.
anonymous
  • anonymous
this is what you do consider \(e^{-x}-x\) on the interval say \([0,1]\)

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anonymous
  • anonymous
at \(x=0\) you get 1 at \(x=1\) you get \(\frac{1}{e}-1\) since 1 is positive, and \(\frac{1}{e}-1\) is negative, by the ivt it must be zero somewhere in between 0 and 1
anonymous
  • anonymous
What does the \ mean?

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