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[數神召喚]Taylor's Inequality
Consider the following function.
f(x) = x sin x, a = 0, n = 4, −0.6 ≤ x ≤ 0.6
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T_4(x) = x^2-1/6*(x^4)
(b) Use Taylor's Inequality to estimate the accuracy of the approximation
f(x) ≈ Tn(x)
when x lies in the given interval (−0.6 ≤ x ≤ 0.6). (Round your answer to four decimal places.)
|R_4(x)| ≤ ?
f(x) = x sin x, a = 0, n = 4, −0.6 ≤ x ≤ 0.6
(a) Approximate f by a Taylor polynomial with degree n at the number a.
T_4(x) = x^2-1/6*(x^4)
(b) Use Taylor's Inequality to estimate the accuracy of the approximation
f(x) ≈ Tn(x)
when x lies in the given interval (−0.6 ≤ x ≤ 0.6). (Round your answer to four decimal places.)
|R_4(x)| ≤ ?
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