Question

3. i. Write second degree Taylor series expansion for f(x) = e^{x^2} function at x_i = 1. And calculate value of this function at x_{i+1} = [2, 1.5, 1.25, 1.1, 1.01, 1.001] points. Make comments about results. ii. Compute f(x) = ln(1 + 2x) at x_{i+1} = 1.1 by first, second, third, and fourth degree Taylor expansions for this function about x_i = 1. Comment about results. (25p)

          3. i. Write second degree Taylor series expansion for f(x) = e^{x^2} function at x_i = 1. And calculate value of this function at x_{i+1} = [2, 1.5, 1.25, 1.1, 1.01, 1.001] points. Make comments about results.

ii. Compute f(x) = ln(1 + 2x) at x_{i+1} = 1.1 by first, second, third, and fourth degree Taylor expansions for this function about x_i = 1. Comment about results. (25p)

3. i. Write second degree Taylor series expansion for f(x) = e^x^2 function at xi = 1. And calculate value of this function at xi+1 = [2, 1.5, 1.25, 1.1, 1.01, 1.001] points. Make comments about results.

ii. Compute f(x) = ln(1 + 2x) at xi+1 = 1.1 by first, second, third, and fourth degree Taylor expansions for this function about xi = 1. Comment about results. (25p)

Added by Erica W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

06/14/2022

Step 1

Given f(x) = ex, the second-degree Taylor series expansion around x = 1 is: f(x) ≈ f(1) + f'(1)(x-1) + f''(1)(x-1)^2 f(1) = e^1 = e f'(x) = e^x, f'(1) = e f''(x) = e^x, f''(1) = e Therefore, the second-degree Taylor series expansion is: f(x) ≈ e + e(x-1) + Show more…

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Write the second-degree Taylor series expansion for the function f(x) = ex when x = 1. Calculate the value of this function at xi+1 [2, 1.5, 1.25, 1.1, 1.01, 1.001] points. Make comments about the results. Compute f(x) = ln(1 + zx) at xi+1 = 1.1 using the first, second, third, and fourth-degree Taylor expansions for this function about xi = 1. Comment on the results.