Use a calculator to estimate the value of f (1.3) = (1.3) * ln(1.3) to 6 decimal places, and find the actual error |Rn (x)| resulting from using your estimates in part (b). How does this actual error compare to the upper bound on the error that you found in part (c)?
Use a calculator to estimate the value of f (1.3) = (1.3) * ln(1.3) to 6 decimal places, and find the actual error |Rn (x)| resulting from using your estimates in part (b). How does this actual error compare to the upper bound on the error that you found in part (c)?
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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Use a calculator to estimate the value of f (1.3) = (1.3) * ln(1.3) to 6 decimal places, and find the actual error |Rn (x)| resulting from using your estimates in part (b). How does this actual error compare to the upper bound on the error that you found in part (c)?
Transcribed Image Text:Step 1: Given
:- 1 +*-1² _ *-1³ + *-1*
fx = x-1 +
Step 2: Approximating the value
fx
x = x - 1 + *-1¹²³_ *-1³ + x*-¹*ƒ1.
Hence f1.3 0.341513
1.3-14
8
+ 1.3-1²_1.3-1³ + ²
f1.3 1.3-1+
= 0.3+
0.09
2
0.027
6
+
0.0081
8
= 0.3+0.045
Transcribed Image Text:The error term in the Taylor series expansion is given by
x-a²
5!
R₁x S -f³ where a is the polynomial centered at aand f = max f³x
as {sx
a = 1, x = 1.3f¹x =
fx attain maximum at = 1.3
R4x ≤ 1.3-15 f5 1.3
5!
Hence the upper bound of the error is 0.0000425
= 4.25 x 10-5
= 0.0000425
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