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j814wong
 3 years ago
Use the intermediate value theorem to show that the equation e^(x)=x has at least one real solution.
j814wong
 3 years ago
Use the intermediate value theorem to show that the equation e^(x)=x has at least one real solution.

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asnaseer
 3 years ago
Best ResponseYou've already chosen the best response.0@j814wong  do you know what the intermediate value theorem states?

j814wong
 3 years ago
Best ResponseYou've already chosen the best response.0Sorry 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.

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0this is what you do consider \(e^{x}x\) on the interval say \([0,1]\)

satellite73
 3 years ago
Best ResponseYou've already chosen the best response.0at \(x=0\) 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
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