106yeah the expression had f(x) on both sides.
btw this is not my dbt :)
If
f(x) = \frac{1}{3}[f(x) + \frac{5}{f(x+2)}]
then \lim_{x\rightarrow \infty }f(x) = ?
edit: f(x) is not a constant function and f(x) > 0 in its domain
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10 Answers
106
11@ Asish
Since lim x→∞ f(x) = lim x→∞ f(x) = lim x→∞ f(x+2) = a (say)
then a = (1/3) (a + 5/a )
THerefore 2 a = 5 / a therefore, a = √(5/2)
Hence lim x→∞ f(x) = √(5/2)
106no ...
analyse the givn condition a bit more . see if u can get a result from it which would automatically reject this answer
btw if the exp was f(x) = 13[f(x+1) + 5f(x+2)
then ur answer wud have been correct
24hey one thing I noticed..this function is periodic with period 4...
I know this has no connection with the ques though :P
106I know this has no connection with the ques though :P
why so??
this was the thing i expected Tushar to notice and it has a strong bearing with the answer
24really ??????
looks like I am near the answer then...
actually i took this observation very lighlty[3]
106see:
as the function is periodic,
f(x) = f(x+4)
So when x→∞, u cant say that f(x) = f(x+2) (as the function is periodic)
So, the answer is
Cant Say..