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A function is given by f(x) = 2x - e-6. Now answer the following: (a) Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h= 1, 0.1, 0.01, 0.0001 in both of the above mentioned methods.

A function is given by f(x) = 2x - e-6. Now answer the following: (a) Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h= 1, 0.1, 0.01, 0.0001 in both of the above mentioned methods.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section: Chapter Questions
Problem 18T
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1. A function is given by f(x) = 2x - e-6. Now answer the following: Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. = (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h above mentioned methods. 1, 0.1, 0.01, 0.0001 in both of the Compute Dat ro = 0.2 using Richardson extrapolation method up to 6 significant figures and calculate the truncation error.
Transcribed Image Text:1. A function is given by f(x) = 2x - e-6. Now answer the following: Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the forward difference method up to 5 significant figures. Approximate the derivative of f(x) at xo = 0.5 with step size h = 0.2 using the central difference method up to 6 significant figures. = (c) (4+4 marks) Calculate the truncation error of f(x) at xo = 2 using h above mentioned methods. 1, 0.1, 0.01, 0.0001 in both of the Compute Dat ro = 0.2 using Richardson extrapolation method up to 6 significant figures and calculate the truncation error.
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