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) ????
I realize that Taylor series f(x)=f(a)+f'(a)(x-a)+f''(a)((x-a)^2)etc...
but the above T(x) is centered at x=2,
BUT I need to know when f(x) is centered at x=0
please assist! thank you!
To approximate f(0) using the given Taylor series T(x), which is centered at x=2, you need to shift the center of the series from x=2 to x=0.
This can be done with a change of variable. Let's call the new variable u = x - 2, so that u represents the difference between the new center (x=0) and the original center (x=2).
Now substitute u into the equation for T(x):
T(x) = 5 - 9(u^2) - 3(u^3)
To find T(0), simply substitute u = 0, because we want to evaluate it at x=0 (the new center):
T(0) = 5 - 9(0^2) - 3(0^3) = 5
Therefore, the approximate value of f(0) using the given Taylor series T(x) centered at x=2 is 5.