Consider the following function.

f(x) = x^2/7, a = 1, n = 3, 0.8 ≤ x ≤ 1.2

(a) approximate f by a taylor polynomial with degree n at the number a. t3(x) =
(b) use taylor's inequality to estimate the accuracy of the approximation f(x) ≈ tn(x) when x lies in the given interval.

(round your answer to eight decimal places.) |r3(x)| ≤

Consider the linear model for a two-stage nested design with b nested in a as given below. yijk=\small \mu + \small \taui + \small \betaj(i) + \small \varepsilon(ij)k , for i=1,; j= ; k=1, assumption: \small \varepsilon(ij)k ~ iid n (0, \small \sigma2) ; \small \taui ~ iid n(0, \small \sigmat2 ); \tiny \sum_{j=1}^{b} \small \betaj(i) =0; \small \varepsilon(ij)k and \small \taui are independent. using only the given information, derive the least square estimator of \small \betaj(i) using the appropriate constraints (sum to zero constraints) and derive e(msb(a) ).