please quickly If the function f(x)=e* is approximated by Lagrange polynomial P3(x) thatinterpolates f at 4 points in the interval [0,1], estimate the error on this interval.O 2.75573 x 10-61.41093 x10-30.002450.11326

Answered: If the function f(x)=e* is approximated…

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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please quickly

If the function f(x)=e* is approximated by Lagrange polynomial P3(x) that
interpolates f at 4 points in the interval [0,1], estimate the error on this interval.
O 2.75573 x 10-6
1.41093 x
10-3
0.00245
0.11326

Expert Solution

Step 1

Linear interpolation is achieved by constructing the lagrange polynomial $p_{3}$ of order 1 , connecting the four pint is given by ,

$P_{3} (x) = L_{0} (x) f (x_{0}) + L_{1} (x) f (x_{1}) + L_{2} (x) f (x_{2}) + L_{3} (x) f (x_{3})$

where,

$L_{0} (x) = (x - x_{1}) (x - x_{2}) (x - x_{3}) / (x_{0} - x_{1}) (x_{0} - x_{2}) (x_{0} - x_{3}) L_{1} (x) = (x - x_{0}) (x - x_{2}) (x - x_{3}) / (x_{1} - x_{0}) (x_{1} - x_{2}) (x_{1} - x_{3}) L_{2} (x) = (x - x_{0}) (x - x_{1}) (x - x_{3}) / (x_{2} - x_{0}) (x_{2} - x_{1}) (x_{2} - x_{3}) L_{3} (x) = (x - x_{0}) (x - x_{1}) (x - x_{2}) / (x_{3} - x_{0}) (x_{3} - x_{1}) (x_{3} - x_{2})$

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