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limit x tends to zero  f(x) + log(1- 1/e^f(x) - log(f(x)) =0

find f(0)

6 years ago

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$\lim_{x\rightarrow 0}f(x) + log( 1 - \frac{1}{e^{f(x)}} - log f(x) = 0$
$f(0) + log( 1 - \frac{1}{e^{f(0)}} - log f(0) = 0$
$-f(0) = log( 1 - \frac{1}{e^{f(0)}} - log f(0)$
$Say f(0) = t$
$e^{-t} = 1 - \frac{1}{e^{t}} - log t$
$e^{-t} = 1 - e^{-t} - log t$
$2 e^{-t} = 1 - log t$
This equation cant be solved using normal methods. Hence, if it is an objective question, you have to put values in it to get the answer. Maybe the question is wrong too.
Thanks & Regards
Bharat Bajaj
IIT Delhi
2 years ago

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