1. Apr 21, 2006

nick727kcin

can someone please let me know whether this is right or wrong please?

here are the directions:

Please find the taylor series for f(x) cntered at the given value of a.

and the question:

f(x)= lnx a= 2

i dont get how to do this since the maclaurin series for ln(x) isnt given....

EDIT: thanks bomba for explaining. can someone just please let me know if this is right or wrong? thanks:

Last edited: Apr 21, 2006
2. Apr 21, 2006

bomba923

Hint:
$$f\left( x \right) = \sum\limits_{n = 0}^\infty {\frac{{f^{\left( n \right)} \left( a \right)}}{{n!}}\left( {x - a} \right)^n }$$

3. Apr 21, 2006

nick727kcin

^thanks

can someone please check it for me? it doesnt look right

4. Apr 21, 2006

HallsofIvy

Staff Emeritus
The formula you have in your first post is clearly incorrect because of that "ln 2". As Bomba told you, the coefficient of (x-2)n is
[itex]\frac{f^{(n)}}{n!}.
f(x)= ln x so f(2)= ln 2: that's the constant term
f'(x)= 1/x f'(2)= 1/2: the coefficient of (x-2) is 1/2 (no ln 2 in it!)
f"(x)= -1/x2 f"(2)= -1/4: the coefficient of (x-2)2 is (-1/4)/2= -1/8.

Can you work out the general term?