Chapter 9.3, Problem 87E

a.

To determine

To approximate: The value $\sqrt[3]{128}$ to within ${10}^{-4}$ of exact value by the method of Taylor polynomial $f\left(x\right)={\left(125+x\right)}^{\frac{1}{3}}$ centered at 0.

b.

To determine

To approximate: The value $\sqrt[3]{128}$ to within ${10}^{-4}$ of exact value by the method of Taylor polynomial $f\left(x\right)={\left(x\right)}^{\frac{1}{3}}$ centered at $125$.

c.

To determine

To compare: The two approaches of a and b are equivalent or not.