2. Consider the function f(x) = x In(x). Now answer the following: (a) Evaluate the numerical derivative of f(x) at x = 1.0 with step size h = 0.1 using the forward and central difference methods up to 5 significant figures. (b) Compute the upper bound of the truncation error of f(x) at x = 1.0 using h = 0.1 for the forward and central difference methods up to 5 significant figures.
2. Consider the function f(x) = x In(x). Now answer the following: (a) Evaluate the numerical derivative of f(x) at x = 1.0 with step size h = 0.1 using the forward and central difference methods up to 5 significant figures. (b) Compute the upper bound of the truncation error of f(x) at x = 1.0 using h = 0.1 for the forward and central difference methods up to 5 significant figures.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Need answer for a and b
![2. Consider the function f(x) = x In(x). Now answer the following:
(a)
Evaluate the numerical derivative of f(x) at x = 1.0 with step size h = 0.1 using the
forward and central difference methods up to 5 significant figures.
Compute the upper bound of the truncation error of f(x) at x = 1.0 using h = 0.1 for
and central difference methods up to 5 significant figures.
(b)
the forward
(c)
Deduce an expression for from D, by replacing h by (4h/3) using the
h
Richardson extrapolation method.
h](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4cd475eb-50e0-41bb-95f1-7312ceac8ee9%2Fa4cffda6-7168-4af7-8062-08e5828a6588%2F6sm8x5k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2. Consider the function f(x) = x In(x). Now answer the following:
(a)
Evaluate the numerical derivative of f(x) at x = 1.0 with step size h = 0.1 using the
forward and central difference methods up to 5 significant figures.
Compute the upper bound of the truncation error of f(x) at x = 1.0 using h = 0.1 for
and central difference methods up to 5 significant figures.
(b)
the forward
(c)
Deduce an expression for from D, by replacing h by (4h/3) using the
h
Richardson extrapolation method.
h
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