Mathematics, 29.01.2020 00:46 olgapagan1010
Find the third taylor polynomial p3(x) for the function f(x) = (x-1)ln(x) about x0 = 1.
(a) use p3(0.5) to approximate f(0.5). find an upper bound for error |f(0.5) - p3(0.5)| using the error formula, and compare it to the actual error.
(b) find a bound for the error |f(x) - p3(x)| in using p3(x) to approximate f(x) on the interval [0.5,1.5].
(c) approximate \int_{0.5}^{1.5}f(x)dx using \int_{0.5}^{1.5}p_{3}(x)dx .
(d) find an upper bound for the error in (c) using \int_{0.5}^{1.5}|r_{3}(x)dx| , and compare the bound to the actual error.
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Find the third taylor polynomial p3(x) for the function f(x) = (x-1)ln(x) about x0 = 1.
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