Refer to the previous problem for context. Suppose you need to integrate some specific function f. From experimental data, you know that f"(x) = e-² and that X -0.5 -0.25 0 0.25 0.5 f(x) 10 8 9 7 11 (a) Calculate the approximation T4 for the integral 0.5 -0.5 f(x) dx to at least 3 decimal places. (b) Find the maximum that the error might be, E(4), for the above approximation to at least 3 decimal places. (c) Combining the previous two parts, determine an interval which is guaranteed to contain the true value of the integral. Provide at least 3 decimal places for the endpoints.
Refer to the previous problem for context. Suppose you need to integrate some specific function f. From experimental data, you know that f"(x) = e-² and that X -0.5 -0.25 0 0.25 0.5 f(x) 10 8 9 7 11 (a) Calculate the approximation T4 for the integral 0.5 -0.5 f(x) dx to at least 3 decimal places. (b) Find the maximum that the error might be, E(4), for the above approximation to at least 3 decimal places. (c) Combining the previous two parts, determine an interval which is guaranteed to contain the true value of the integral. Provide at least 3 decimal places for the endpoints.
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:8. Refer to the previous problem for context. Suppose you need to integrate some specific
function f. From experimental data, you know that f"(x) = e-² and that
x -0.5 -0.25 0 0.25 0.5
f(x) 10
8 9 7 11
(a) Calculate the approximation T4 for the integral
9. Determine, with full justification, if
0.5
(b) Find the maximum that the error might be, E(4), for the above approximation to at
least 3 decimal places.
∞
-0.5
(c) Combining the previous two parts, determine an interval which is guaranteed to contain
the true value of the integral. Provide at least 3 decimal places for the endpoints.
e-2
f(x) da to at least 3 decimal places.
de converges.
(1 m) separately, as in problem 18 from the
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