lim (x-> 0) [f(x)+log {1-(1/ef (x))}-log (f(x))]=0.
Find f (0).
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1 Answers
13Lim (x->0) [ f(x) + log{1-1/ef(x) - log(f(x))}]
Lim (x->0) [f(x) + log[ {1-1/ef(x)} /f(x)]
Lim(x->0) [f(x) + log [ {ef(x)-1} / { f(x). ef(x)}] ]........as we know that lim(x->0) [ex-1/x ]= 1.....so
Lim(x->0) [ f(x) + log { 1/ef(x)} ]
Lim(x->0) [ f(x) + log 1 - log{ ef(x) }]
Lim(x->0) [f(x) - log{ ef(x)} ] = 0
Now putting 0 we get f(0)=log [ ef(0)]
Soumyadeep Basu Here x tends to zero. It is not given that f(x) tends to zero.Upvote·0· Reply ·2013-06-16 19:16:09- Soumyadeep Basu Actually, f(0)=0.