4. Given data of f(x) = ln(e" +2) in the following table -1 -0.5 0.5 f(x) | 0.86199480 0.95802009 | f'(x) | 0.15536240 | 0.23269654 | 0.33333333 0.45186776 1.0986123 1.2943768 (i) Construct the Lagrange interpolating polynomial of degree three and use it to approximate f(0.25); (ii) Construct the Hermite interpolating polynomial of degree five (through using xo = -0.5, x1 = 0 and x2 = 0.5) and use it to approximate f(0.25). %3D
4. Given data of f(x) = ln(e" +2) in the following table -1 -0.5 0.5 f(x) | 0.86199480 0.95802009 | f'(x) | 0.15536240 | 0.23269654 | 0.33333333 0.45186776 1.0986123 1.2943768 (i) Construct the Lagrange interpolating polynomial of degree three and use it to approximate f(0.25); (ii) Construct the Hermite interpolating polynomial of degree five (through using xo = -0.5, x1 = 0 and x2 = 0.5) and use it to approximate f(0.25). %3D
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
![4. Given data of f(x) = ln(e" + 2) in the following table
-1
-0.5
0.5
f (x)
f'(x) | 0.15536240 | 0.23269654
0.86199480 | 0.95802009
1.0986123
1.2943768
0.33333333 0.45186776
(i) Construct the Lagrange interpolating polynomial of degree three and use it to approximate
f(0.25);
(ii) Construct the Hermite interpolating polynomial of degree five (through using xo =
x1 = 0 and x2 = 0.5) and use it to approximate f(0.25).
Note: Use 8-digit rounding in calculations.
-0.5,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc93be347-1a0a-4c78-aca0-c94abc3e4570%2Fe05f0827-8d37-4d35-936a-d0cd9802b4a7%2F6c5n357_processed.jpeg&w=3840&q=75)
Transcribed Image Text:4. Given data of f(x) = ln(e" + 2) in the following table
-1
-0.5
0.5
f (x)
f'(x) | 0.15536240 | 0.23269654
0.86199480 | 0.95802009
1.0986123
1.2943768
0.33333333 0.45186776
(i) Construct the Lagrange interpolating polynomial of degree three and use it to approximate
f(0.25);
(ii) Construct the Hermite interpolating polynomial of degree five (through using xo =
x1 = 0 and x2 = 0.5) and use it to approximate f(0.25).
Note: Use 8-digit rounding in calculations.
-0.5,
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