Question # 55: Consider the following data set: X f(x) -0.1 -0.09483 0 0 for a function f (x) For these data values answer the following, and write all your results up to five decimal places. 3. 1. Using the above data, compute the first derivative of the function numerically by using the central difference method. 2. I For in interval [-0.1, 0.1], compute the error bound (truncation error) if the above data is generated by the function, f(x) = e¯ + 2x −. 1 X 1 Also compute the actual error. 4. . Based on your error calculations in the previous two parts, explain why the result found for the numerical value of the first derivative in the first part of the question is acceptable or not. 0.1 0.10484
Question # 55: Consider the following data set: X f(x) -0.1 -0.09483 0 0 for a function f (x) For these data values answer the following, and write all your results up to five decimal places. 3. 1. Using the above data, compute the first derivative of the function numerically by using the central difference method. 2. I For in interval [-0.1, 0.1], compute the error bound (truncation error) if the above data is generated by the function, f(x) = e¯ + 2x −. 1 X 1 Also compute the actual error. 4. . Based on your error calculations in the previous two parts, explain why the result found for the numerical value of the first derivative in the first part of the question is acceptable or not. 0.1 0.10484
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 # 55: Consider the following data set:
-0.1
0.1
f (x)
-0.09483
0.10484
for a function f (x) For these data values answer
the following, and write all your results up to five
decimal places.
Using the above data, compute the
first derivative of the function numerically by
1.
using the central difference method.
For in interval -0.1,0.1], compute
2. Į
the error bound (truncation error) if the above
data is generated by the function,
f (x) = e-* + 2x – 1
3.
T Also compute the actual error.
4.
Based on your error calculations in
the previous two parts, explain why the result
found for the numerical value of the first
derivative in the first part of the question is
acceptable or not.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F87ad2ca8-d66d-4e75-84b8-141a4dbbd1f2%2F08abf786-2449-43dc-975e-c01a1903b971%2Fx30qu6_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question # 55: Consider the following data set:
-0.1
0.1
f (x)
-0.09483
0.10484
for a function f (x) For these data values answer
the following, and write all your results up to five
decimal places.
Using the above data, compute the
first derivative of the function numerically by
1.
using the central difference method.
For in interval -0.1,0.1], compute
2. Į
the error bound (truncation error) if the above
data is generated by the function,
f (x) = e-* + 2x – 1
3.
T Also compute the actual error.
4.
Based on your error calculations in
the previous two parts, explain why the result
found for the numerical value of the first
derivative in the first part of the question is
acceptable or not.
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