Thread: approximating error on taylor poly

Find the fifth order taylor polynomial for f(x) = 1/x^2 based at x_0 = 1, then find an interval centered at x_0 = 1 in which the approximation error |f(x) - P_5(x)| < 0.01

I found the taylor poly
1 -2(x-1) + 3(x-1)^2 -4(x-1)^3 ... -6(x-1)^5

I don't know how to simply find the approximation. I could try solving for x but that would take way too long.

Originally Posted by diroga

I found the taylor poly
1 -2(x-1) + 3(x-1)^2 -4(x-1)^3 ... -6(x-1)^5

I don't know how to simply find the approximation. I could try solving for x but that would take way too long.

The error in an alternating series is always less than the n+1 term

Hello,

You have an expression of the rest :

After having calculate this integral we obtain :



Then you study this function on for example.

And we find this interval :

Maybe it exists an easier solution.

Edit : Yes, I didn't think to use series...