Question

How do you do this question?

Answer 1

Step-by-step explanation:

Find the next term of the Taylor series.

f⁽⁰⁾(x) = x^⅓

f⁽¹⁾(x) = ⅓ x^-⅔

f⁽²⁾(x) = -²/₉ x^-⁵/₃

f⁽³⁾(x) = ¹⁰/₂₇ x^-⁸/₃

f⁽⁴⁾(x) = -⁸⁰/₈₁ x^-¹¹/₃

So the fourth term would be:

(-⁸⁰/₈₁ z^-¹¹/₃) (x − 1)⁴ / 4!

For 0.8 ≤ z ≤ 1.2, │f⁽⁴⁾(z)│is a maximum at z = 0.8.  Therefore:

│R₃(x)│≤ │(-⁸⁰/₈₁ (0.8)^-¹¹/₃) (0.8 − 1)⁴ / 4!│

│R₃(x)│≤ 0.00014923

Looks like you accidentally wrote an extra zero.