Understanding Laws for O(x^n) Objects | Tailor Series Question

[transgalactic]

i added a link with my question and how i tried to solve it

i have problen in the laws involved in o(x^n) object

http://img265.imageshack.us/my.php?image=img8133lz0.jpg

 

[HallsofIvy]

I cannot open that web-page.

 

[transgalactic]

i uploaded again the page here

http://img183.imageshack.us/my.php?image=img8133dy8.jpg

is that ok now??

 

[HallsofIvy]

Your very first statement is wrong. The Taylor's (not "tailor") series for ln(1+ x) is NOT alternating. You also write x^3/3= 2x^3/6= 2x^3/3! and x^4/4= 6x^2/(4*6)= 6x^4/4! and then, for some reason, drop the "2" and "6" in the numerator in the next line.

 

[Gib Z]

What power do I need to open up the series to, because I have an x^5 term, which contradicts O(x^4)

Do you actually know what O(x^4) means? If you do, that problem is extremely easy.

 

[transgalactic]

besides those mistakes with the numenator numbers
i tried to build the tailor series of both function from scrach
where did i go wronge in the process

 

[Gib Z]

No offense but lately it seems you've been trying to use and do a lot of things with Taylor series, but you should really learn the fundamentals first. Taking Taylor series 'from scratch' involves taking derivatives, making bounds on the remainder etc etc. What you are doing is basically badly manipulating series. Tell us what mathematics you know and what you want to know, and we'll tell you what you need to learn to fill in the gaps.

 

[transgalactic]

ok,
as i showed in the link

first i tried to build the series of each function

till x^4 power(thats what was given in the question )
i made 4 derivatives of each function
and built a series by making f(0)+f'(0)x +(f''(0)x^2)/2+(f'''(0)x^2)/6 +(f''''(0)x^2)/24 +o(x^4)

then the lan series needed to be multiplied by x
so i increased by 1 the power of each object in the lan series except the remainder

and now i substituted each object in the e^t series with the series on the lan
i have built

the problem is
i was tald to build till the 4th power
but by making the x multiplication previosly i got x^5 object

also i was told that the expresion i got after the substitution
doesnt need to be opened by the formula formula (a+b)^2
but we only wright the object which are defined bellow the power of the remainder
we right objects which are in the power of 4 or less

this is my knowledge about this question
where did i get it wronge?

 

[transgalactic]

my problem is with x^5 object that i got

my dilema is

either to develop the series to the grade for which
even after making the multiplication by x it won't go over x^4
but in this case after the multiplication
the o(x^4) changes to o(x^5)

the other way is to delete the x^5
because our question asks us for series till the 4th power

but here again the o(x^4) changes to o(x^5) after multiplication by x

??