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Grade 11Differential Calculus

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

find f(0)

Profile image of tushar a
16 Years agoGrade 11
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1 Answer

Profile image of bharat bajaj
12 Years ago
\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
askiitian faculty
IIT Delhi

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