Math Is Fun Forum

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Little oh help!!!

Hi guys,

I need help with this:

Given the function f(x)=

Find the real numbers a and b such that

f(x)=lxl*(a+b/x+o(1/x))

As x goes to infinity.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Little oh help!!!

Can anyone help? I think a big Oh can replace the little oh.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

hammana

Member

Registered: 2012-03-02

Posts: 48

Re: Little oh help!!!

aproximate f(x) by ax+b, calculate the two most significant terms of (ax+b)^4
coefficient of x^4  =  a^4 should equal 1
coeficient of x^3=2* b*a^3 should equal 8
therefore a=1, b=2
It means that as x increses the fuction f(x) aproaches the straitht line y=x+2
To know whether it is above or below, you should use y=ax+b+c/x
It happens in this case that c=0, we must go to y=ax+b+d/x*x
I find d=-2 (assuming  my calculations are right) which means that f(x) is below y=x+2 for x positive
and above for x negative.
It is more professional to use the newton formula (1+a)^m= 1+m*a+m*(m-1)/2*(a^2) etc  which is still
valid for non integral valus of m
( m=.25 in this case) but the calculations are more awkward.
I hope I have been clear enough other wise call back