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A. What type of errors occurs when using a numerical method (i.e., the Taylor Series)? B. In general, how can the error of an estimated value using the Taylor Series be minimized? C. Why did the error increase after reducing the step size (h) in the above situation? Explain it.

A. What type of errors occurs when using a numerical method (i.e., the Taylor Series)? B. In general, how can the error of an estimated value using the Taylor Series be minimized? C. Why did the error increase after reducing the step size (h) in the above situation? Explain it.

Advanced Engineering Mathematics
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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Question #01 Please provide justified answer asap for all sub parts
1- A student has used the Taylor Series to estimate the output of a function at a specific point (i.e., f(x2)). They kept reducing the step size (h=x2-x1) to decrease the error (e) of the estimates. However, at one point, they noticed that the error is increasing instead of decreasing, as reported below. h 2 1.5 0.75 0.25 0.125 Error (&) 10% 6% 5% 7% 9% A. What type of errors occurs when using a numerical method (i.e., the Taylor Series)? B. In general, how can the error of an estimated value using the Taylor Series be minimized? C. Why did the error increase after reducing the step size (h) in the above situation? Explain it. CS Scanned with CamScanner
Transcribed Image Text:1- A student has used the Taylor Series to estimate the output of a function at a specific point (i.e., f(x2)). They kept reducing the step size (h=x2-x1) to decrease the error (e) of the estimates. However, at one point, they noticed that the error is increasing instead of decreasing, as reported below. h 2 1.5 0.75 0.25 0.125 Error (&) 10% 6% 5% 7% 9% A. What type of errors occurs when using a numerical method (i.e., the Taylor Series)? B. In general, how can the error of an estimated value using the Taylor Series be minimized? C. Why did the error increase after reducing the step size (h) in the above situation? Explain it. CS Scanned with CamScanner
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