Consider the following function.
\(f(x) = x^{2/5}\), \(a = 1\), \(n = 3\), \(0.8 \le x \le 1.2\)
(a) Approximate \(f\) by a Taylor polynomial with degree \(n\) at the number \(a\).
\(T_3(x) = \frac{8x^3}{125} - \frac{39x^2}{125} + \frac{104x}{125} + \frac{52}{125}\)
(b) Use Taylor's Inequality to estimate the accuracy of the approximation \(f(x) \approx T_n(x)\) when \(x\) lies in the given interval. (Round your answer to eight decimal places.)
\(|R_3(x)| \le 0.10000803\)