exercise (b)\nuse taylors inequality to estimate the accuracy of the approximation f ≈ tn(x) when x lies in…

exercise (b)\nuse taylors inequality to estimate the accuracy of the approximation f ≈ tn(x) when x lies in the given interval.\nstep 1\nif |f^(4)(x)| ≤ m, then we know that\n|r3(x)| ≤ m / 4! |x|^4.\nstep 2\nif we have 0 ≤ x ≤ 0.2, then we have |x| ≤, which means that |x|^4 ≤.\nsubmit skip (you cannot come back)\nexercise (c)\ncheck your result in part (b) by graphing |rn(x)|.

exercise (b)\nuse taylors inequality to estimate the accuracy of the approximation f ≈ tn(x) when x lies in the given interval.\nstep 1\nif |f^(4)(x)| ≤ m, then we know that\n|r3(x)| ≤ m / 4! |x|^4.\nstep 2\nif we have 0 ≤ x ≤ 0.2, then we have |x| ≤, which means that |x|^4 ≤.\nsubmit skip (you cannot come back)\nexercise (c)\ncheck your result in part (b) by graphing |rn(x)|.

Answer

Explanation:

Step1: Analyze the absolute - value range of x

Given (0\leq x\leq0.2), the absolute - value of (x) satisfies (|x|\leq0.2).

Step2: Calculate the upper - bound of (|x|^4)

If (|x|\leq0.2), then (|x|^4\leq(0.2)^4 = 0.0016).

Answer:

First blank: (0.2) Second blank: (0.0016)