Let xo = 0.5. Given 1 f(x) = -2ex + 4x² ELL f'(x) = 2e-x + x³ 1 1 1 120 x -x5 + 2x 24 1 ƒ"(x) = −2e¯* + 3x²-x f(4)(x) = -2e-* +6-x f(5)(x) = 2e-x-1 f(6)(x) = -2e-* 6 + 2 1 2 f''(x) = 2e-x + 6x - x² 2 x3 a. Find the Taylor Polynomial, T3 (x), of degree at most 3 for f(x) expanded about xo. b. Give the general error formula for f(x) - T3(x) for any x. c. Find the absolute error in using T3 (0.65) to approximate f(0.65). d. Use the error formula to find a bound for the absolute error in approximating f (0.65) with T3 (0.65).

Let xo = 0.5. Given 1 f(x) = -2ex + 4x² ELL f'(x) = 2e-x + x³ 1 1 1 120 x -x5 + 2x 24 1 ƒ"(x) = −2e¯* + 3x²-x f(4)(x) = -2e-* +6-x f(5)(x) = 2e-x-1 f(6)(x) = -2e-* 6 + 2 1 2 f''(x) = 2e-x + 6x - x² 2 x3 a. Find the Taylor Polynomial, T3 (x), of degree at most 3 for f(x) expanded about xo. b. Give the general error formula for f(x) - T3(x) for any x. c. Find the absolute error in using T3 (0.65) to approximate f(0.65). d. Use the error formula to find a bound for the absolute error in approximating f (0.65) with T3 (0.65).

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

See similar textbooks