The approximate expression for the second derivative of the function f(x) is: f'(x) = (f(x-h)-2 f(x) + f(x+h) ) / h². 7. Find the true error and relative true error when this expression is used to estimate the second derivative off(x)=e².5x + 25x at x=0 with h=1/3. Give your answers to 4 significant digits. Find the absolute approximate error and absolute relative approximate error when this expression is used to estimate the second derivative of f(x)-e2.5x + e2.5x at x=0 with h=1/4 and h=1/8. Give your answers to 4 significant digits. 8.
The approximate expression for the second derivative of the function f(x) is: f'(x) = (f(x-h)-2 f(x) + f(x+h) ) / h². 7. Find the true error and relative true error when this expression is used to estimate the second derivative off(x)=e².5x + 25x at x=0 with h=1/3. Give your answers to 4 significant digits. Find the absolute approximate error and absolute relative approximate error when this expression is used to estimate the second derivative of f(x)-e2.5x + e2.5x at x=0 with h=1/4 and h=1/8. Give your answers to 4 significant digits. 8.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please do exercise 7 and 8 and please show work
Transcribed Image Text:The approximate expression for the second derivative of the function f(x) is:
f'(x) = (f(x-h)-2 f(x) + f(x+h)) /h².
7. Find the true error and relative true error when this expression is used to estimate the second
derivative of f(x)=e².5x + e2.5x at x=0 with h=1/3. Give your answers to 4 significant digits.
Find the absolute approximate error and absolute relative approximate error when this expression
is used to estimate the second derivative of f(x)=e².5x + e2.5x at x=0 with h=1/4 and h=1/8. Give
your answers to 4 significant digits.
8.
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