1st degree taylor polynomial question

[pakmingki]

Homework Statement

find an interval I such that the tangent line error bound is always less than or equal to 0.01 on I

f(x) = ln(x)
b = 1

The Attempt at a Solution

so basically, i found the tangent line approximation at b = 1, which is t(x) = x -1.

From there though, i have no idea how to continue.
I figured out that abs[f(x) - t(x)]is always supposed to be less than 0.01 on I, but i have no idea how to find I.

thanks alot.

 

[Dick]

I think you'll want to think about writing down some form of remainder term for the taylor series. There are several. Which one are you expected to use?