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Consider the following function. f(x) = ln(1 + 2x),    a = 1,    n = 3,    0.8 ≤ x ≤...

Consider the following function.

f(x) = ln(1 + 2x),    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 six decimal places.)

|R3(x)| ≤

(c) Check your result in part (b) by graphing |Rn(x)|.

Math   Calculus   
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