# calculus

posted by .

how do i use a taylor series centered at some x value to approximate the value of the function centered at a different x value?
for example, if im given some taylor series centered at 5 of f(x) but i want to find f(3), how do i do this? (btw that example is not my homework problem, i'm just trying to understand the method)

thanks alot!

• calculus -

It depends on the radius of convergence. If the series has a radius of convergence of ∞ such as the series for sin(x), cos(x), and exp(x), you can evaluate f(x) where x equals any defined value, even though the series are expanded about an arbitrary value x0. In the three examples cited above, they are expanded around 0.

If the radius of convergence is small, and the desired evaluation point is not within the radius of convergence, then you'll need to expand the series about an appropriate point. But then you'll also need to calculate f'(x0), f"(x0), .... but that's part of the game of series expansion.

## Similar Questions

1. ### Taylor seires

f(x) =ln (1-x) a) Compute f'(x), f''(x), f'''(x). Spot the pattern and give an expression for f ^(n) (x) [the n-th derivative of f(x)] b) Compute the MacLaurin series of f(x) (i.e. the Taylor series of f(x) around x=0) c) Compute the …
2. ### Calculus - Taylor #2

Find the Taylor series for f(x) centered at the given value of 'a'. (Assume that 'f' has a power series expansion. Do not show that Rn(x)-->0.) f(x) = x3, a = -1 and what i've done so far: f (x) = x^3 f ' (x) = 3x^2 f '' (x) = 6x^1 …
3. ### Math

Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ?
4. ### calculus repost, please assist pleassssssse

Hi Trying to work with confusing Taylor series....any assistance would be much appreciated!! How can I use T(x)=5-9((x-2)^2)-3((x-2)^3) to approximate the f(0) ?
5. ### Calc 2 taylor series

use the definition of a taylor series to find the Taylor series (centeredat c) for the function. f(x)= 7/x c=1 so what is f(x) as n goes from 0 to infinity?
6. ### Calculus

Find the first four non-zero terms and the general term for the Taylor Series centered at c = 1 for the integral of ln(x).
7. ### Calculus

By recognizing each series below as a Taylor series evaluated at a particular value of x, find the sum of each convergent series. A) 1+5 + (5^2)/(2!)+(5^3)/(3!)+(5^4)/(4!)+...+ (5^k)/(k!)+...= B) 1-(2^2)/(2!)+(2^4)/(4!)-(2^6)/(6!)+...+((-1)^(k)2^(2k))/((2k)!) …
8. ### Maths

Use the binomial series to find the Taylor series about 0 for the function f(x) = (1 + x)−3/5, giving all terms up to the one in x4. I have the answer; f(x)=1-3/5(x) +12/25(x^2) -52/125(x^3) + 234/625(x^4) but i am not sure how …
9. ### Urgent help Maths Ms sue

Use binomial series to find the Taylor series about 0 for the function f(x)=(1+x)^-3/5 giving all terms up to the one in x^4. Then use this series and Taylor series for sin x to find the quartic Taylor polynomial about 0 for the function …