Write down the the cardinal functions for these 5 nodes , and use the Lagrange polynomials to interpolate these 5 nodes, show the polynomial.
Write down the the cardinal functions for these 5 nodes , and use the Lagrange polynomials to interpolate these 5 nodes, show the polynomial.
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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Write down the the cardinal functions for these 5 nodes , and use
the Lagrange polynomials to interpolate these 5 nodes, show the polynomial.
![**Theoretical Assignment**
Consider the hyperbolic tangent function:
\[
\tanh(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)}
\]
where \( x \in [-2, 2] \). Use 5 nodes to uniformly divide the interval \([-2, 2]\) into 4 sub-intervals.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F015fa499-4229-4065-9077-9d1ac4317e71%2Fe7964c81-e0f9-46af-b6a1-856225e68aea%2Fqw95hij_processed.png&w=3840&q=75)
Transcribed Image Text:**Theoretical Assignment**
Consider the hyperbolic tangent function:
\[
\tanh(x) = \frac{\exp(x) - \exp(-x)}{\exp(x) + \exp(-x)}
\]
where \( x \in [-2, 2] \). Use 5 nodes to uniformly divide the interval \([-2, 2]\) into 4 sub-intervals.
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