I need the answers for the 2 boxes with the red x checked by them. Thank you. Ro

Question

I need the answers for the 2 boxes with the red x checked by them. Thank you. Round to 5 decimal places please.

Consider the following function. f (ar) 0. n 3.0 0.2 Exercise (a) Approximate f by a Taylor polynomial with degree n at the number a Part 1 of 3 The Taylor polynomial with degree n 3 is a)(x a The function f(x) 4x2 has derivatives e 4x2 f (x) 8ar 4x2 and 64 r2 8 Pe f (x) 3 4x2 f (x) 512x 192x 512r 192r Part 2 of 3 With a 0, f(0) J 1 1 f (0) 0 Part 3 of 3 Therefore (x) 1 4x 8 and f "(0) 30.

Explanation / Answer

M= f 4(0.2) = [ 4096(.2)4=3072(.2)2+ 192 ]e0.16

= 321.4336 x 1.1735

| R3(x) |< M x4/ 4! = 321.4336 x1.1735x0.0016 / 24 = 0.025

| R3(x)| < 0.025

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