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?