# Thread: approximations using Taylor sries

1. ## approximations using Taylor sries

I hear you could use taylor polynomials or series to approximate things like $\sqrt9.04$ for example or something like that...is that true and how can that be done?

post number 100 yay!!!!

2. Originally Posted by akhayoon
I hear you could use taylor polynomials or series to approximate things like $\sqrt9.04$ for example or something like that...is that true and how can that be done?

post number 100 yay!!!!
The Taylor series for a function $f$ about $x$ can be writen:

$f(x+\varepsilon)=f(x)+\varepsilon f'(x) + \left(\frac{\varepsilon}{2}\right)^2f''(x)+ ... + \left(\frac{\varepsilon}{n!}\right)^nf^{(n)}(x)+ ...$

In your case $f(x)=x^{1/2}$ , and so we have:

$
(9.04)^{1/2} \approx (9)^{1/2}+0.04 \times (1/2) \times 9^{-1/2} - 0.04^2 \times (1/8) \times 9^{-3/2} ...

$

Which is pretty good even after just the first two terms

RonL