| Author |
Message |
![[Post New]](/templates/default/images/icon_minipost_new.gif) 9 Jun 2008 13:20:45 IST
|
|
|
f(x+y)=f(x).f)(y) for all x
f'(0)=2
determine f(x)
|
|
|
|
9 Jun 2008 13:24:52 IST
|
|
|
f(x) is a function of x....hope i helped u...
|
<TABLE CELLSPACING="1" CELLPADDING="1" BORDER="0">
<TR><TD>
      
<DIV ALIGN="right">Glitter Graphics</DIV></TD></TR></TABLE>
if i helped u plzzzzz rate me,,,,,,, |
this reply: 5 points
(with 1 
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
9 Jun 2008 13:37:22 IST
|
|
|
as
f(x+y)=f(x).f(y)
f(x) is of the form a^x
f'(0)=2
f'(x)=(a^x)ln(a)
f'(0)=ln(a)=2
a=e^2
so...f(x)=e^(2x)
hope it helps....cheero :)
|
Who says nothing is impossible.
I've been doing nothing for years !!..............
I know KUNG FU KARATE
and 47 other dangerous words.............
|
this reply: 0 points
(with 0
in 0 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
9 Jun 2008 13:38:55 IST
|
|
|
First let us find f(0).Puy x=y=0,we get f(0)=0 or 1.
If f(0)=0 then put x=x,y=0,we get f(x)=0 and f'(x)=0 which is not true as f'(0)=2.
Hence,f(0)=1.Now, as it is given f'(0)=2.
  using the above result.
Hence,f'(x)=2f(x) then f'(x)/f(x)=2.
Now taking integral on both sides,we get,
lnIf(x)I=2x+c where c=0 as f(0)=1
Hence,f(x)=e2x.
|
MAKING A MISTAKE IS HUMAN BUT REPEATING IT IS IDIOTIC. |
this reply: 5 points
(with 1
in 1 votes ) [?]
|
|
You have to be logged on to rate
|
|
|
|
|
Moderation Team
![[Up]](/templates/default/images/icon_up.gif "[Up]"){kind=icon}
2
