Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I have $b>a$ and an invertible and infinitely differentiable function $f$. If I want to evaluate $\epsilon=f^{-1}(b-a)$ by writing:
$b\approx a+f'(a)\epsilon+f''(a)\epsilon^2/2+f''(a)\epsilon^3/6+\cdots+f^{(n)}(a)\epsilon^n/n!$
and solving the polynomial equation for $\epsilon$, what is the error incurred?

Paraphrasing, if I call the approximate value of $\epsilon$ evaluated by solving an $n$th order polynomial equation $\epsilon_n$ then is it true that:


share|cite|improve this question

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.