Question

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)|.

Name: consider the following function fx ln1 2x a 1 n 3 08 x 12 a approximate f by a taylor polynomial with degree n at the number a t3x b use taylors inequality to estimate the accuracy of the ap 53851
Uploaded: 2023-07-23T14:59:34-08:00
Duration: 3 min 42 s
Channel: Adi S
Description: consider the following function fx ln1 2x a 1 n 3 08 x 12 a approximate f by a taylor polynomial with degree n at the number a t3x b use taylors inequality to estimate the accuracy of the ap 53851

          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)|.

Added by Ashley W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

07/23/2023

Step 1

f(x) = ln(1 + 2x) f'(x) = (1/(1 + 2x)) * 2 = 2/(1 + 2x) f''(x) = -4/(1 + 2x)^2 f'''(x) = 24/(1 + 2x)^3 Now, evaluate these derivatives at x = 1: f(1) = ln(1 + 2(1)) = ln(3) f'(1) = 2/(1 + 2(1)) = 2/3 f''(1) = -4/(1 + 2(1))^2 = -4/9 f'''(1) = 24/(1 + 2(1))^3 = Show more…

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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)|.