Q1. (a) Estimate the value of the function f(x) = ex at x = 1 using...

 

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Q1. (a) Estimate the value of the function f(x) = e²x at x = 1 using a Taylor's series expansion of the function about a = 0. Use three terms only. (b) Determine the relative error of your estimate in percentage. Q2. Considering the initial approximation x = 1 for the root of f(x) = 2(x² − 4) = 0, (a) Calculate the root after three iterations using Newton-Raphson's Method (b) Calculate the approximate error in (a) Q1. (a) Estimate the value of the function f(x) = e²x at x = 1 using a Taylor's series expansion of the function about a = 0. Use three terms only. (b) Determine the relative error of your estimate in percentage. Q2. Considering the initial approximation x = 1 for the root of f(x) = 2(x² − 4) = 0, (a) Calculate the root after three iterations using Newton-Raphson's Method (b) Calculate the approximate error in (a)