How Can I Use the Mean Value Theorem to Solve Equations with O Notation?

[transgalactic]

a question that i tried to solve it before

my new solution in the link


http://img184.imageshack.us/my.php?image=img8222mk2.jpg


now i solved it like in the method of the last post

i develeloped the ln series till the x^2 power
the "e" series to the second power too

when i multiplied the lan series by x i added 1 to the O member

and i cut down in the end all the members which are bigger then the 4th power

now i got the solution to this question and i can't see no subtitution
in there
he is not adding 1 to the "O" object when multiplying the series by x

and he gets all the points

i don't care if you too don't get any sense in it

where did i go wrong?

 

[Gib Z]

You only expanded some series to their 2nd term, how do you expect to get an error on the order of x^4?

 

[transgalactic]

so your saying that i should expand each one of the serieses to the 4th term
(even if the last term is zero)
like the sinus function

?

what about the multiplication by x of a series
does it changes the "O" object ?

 

[transgalactic]

here is my new solution to the question

is it ok?

its still doesn't comeout as the solution in the book

http://img158.imageshack.us/my.php?image=img8223br3.jpg

 

[Rainbow Child]

is it ok?

its still doesn't comeout as the solution in the book

http://img158.imageshack.us/my.php?image=img8223br3.jpg

Three errors.

The coefficient of u^3 is 5/81.
The coefficient of u^4 is -10/243.
You forgot the term -\frac{4}{9}\,x^2 in the final answer

 

[Rainbow Child]

a question that i tried to solve it before

my new solution in the link


http://img184.imageshack.us/my.php?image=img8222mk2.jpg


now i solved it like in the method of the last post

i develeloped the ln series till the x^2 power
the "e" series to the second power too

when i multiplied the lan series by x i added 1 to the O member

and i cut down in the end all the members which are bigger then the 4th power

now i got the solution to this question and i can't see no subtitution
in there
he is not adding 1 to the "O" object when multiplying the series by x

and he gets all the points

i don't care if you too don't get any sense in it

where did i go wrong?

As Gib said you should write \ln(1+x) till 3^rd power, in order to pick up a x⁴ term in x\,\ln(1+x) expansion

 

[transgalactic]

gib said that i should expand both of them till the 4th power
in order to get the error of the 4th power


but
ok
i'll try to solve it again like that

but do i need to add 1 to the "O" member from O(x^3) >>> O(x^4)

 

[Rainbow Child]

No you don't. You write the series as it is.

 

[transgalactic]

here is the solution of this question

and he did it not by your rule of "developing the series till the 3rd power"

and he got all the point

http://img218.imageshack.us/my.php?image=img8222tr6.jpg

what is this solution??
he didnt do like you told me

why ?
is it a wrong solution??

 

[Rainbow Child]

He developed the \ln(1+x) till the 4th power and kept the terms in x\,\ln(1+x) till the 4th power, i.e. the 3rd power of \ln(1+x).

What's the question about my post?

Develope till the 3rd power is enough. Isn't it clear?

 

[transgalactic]

ahhhhh ok thanks ill try to solve it again
and the other question too

 

[Gib Z]

No offence but do you actually know what exactly Big -Oh notation is? Are you familiar with the mean value theorem? If you are, you should have no problem with these, which you are.

 

[transgalactic]

whats the link of the mean value theorem with the O notation??