Consider the polynomial f(x)=5x-2-5x2. Using the forward divided difference approximation for the first derivative with step size h=2 we get f' (-2,5)-20. Divide the step size in half successively until you get a step size small enough to get an approximation of f'(x) correct to at least two significant figures. That is, you have to approximate f'(-2.5) with h=1,0.5,0.25,.. You cannot use the exact value of f(-2.5) to determine the answer. The step size h= it is enough to have at least two correct significant figures in the approximation of f'(x). The corresponding approximation is f'(-2,5)=. and the percentage approximate relative absolute error is lɛal= % Note: To have a correct result in at least n significant figures, it is enough that Jea|s(0.5x102-n)%.
Consider the polynomial f(x)=5x-2-5x2. Using the forward divided difference approximation for the first derivative with step size h=2 we get f' (-2,5)-20. Divide the step size in half successively until you get a step size small enough to get an approximation of f'(x) correct to at least two significant figures. That is, you have to approximate f'(-2.5) with h=1,0.5,0.25,.. You cannot use the exact value of f(-2.5) to determine the answer. The step size h= it is enough to have at least two correct significant figures in the approximation of f'(x). The corresponding approximation is f'(-2,5)=. and the percentage approximate relative absolute error is lɛal= % Note: To have a correct result in at least n significant figures, it is enough that Jea|s(0.5x102-n)%.
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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Transcribed Image Text:Consider the polynomial
f(x)=5x-2-5x2.
Using the forward divided difference approximation for the first derivative with step size h=2 we get f'
(-2.5)-20. Divide the step size in half successively until you get a step size small enough to get an
approximation of f'(x) correct to at least two significant figures. That is, you have to approximate f'(-2.5)
with h=1,0.5,0.25,... You cannot use the exact value of f'(-2.5) to determine the answer.
The step size h=
it is enough to have at least two correct significant figures in the approximation of f(x). The
corresponding approximation is f'(-2.5)-
and the percentage approximate relative absolute error is Jɛal=
%
Note: To have a correct result in at least n significant figures, it is enough that
|ɛa|s(0.5x102-n)%.
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