please quicklyASAAAP Consider the Lagrange polynomial that passes through the 4 data points givenby278y7 151 | 407 | 601Then Lo (x)= at x=4 is given by-4/54/31/32/15

We know that L0x is given by L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3 1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Answered: Consider the Lagrange polynomial that…

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

ASAAAP

Consider the Lagrange polynomial that passes through the 4 data points given
by
2
7
8
y7 151 | 407 | 601
Then Lo (x)= at x=4 is given by
-4/5
4/3
1/3
2/15

Expert Solution

Step 1

We know that $L_{0} (x)$ is given by

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

Here, $x_{0} = 2, x_{1} = 5, x_{2} = 7, x_{3} = 8, x = 4$

Putting all these values in (1), we get

$L_{0} (x) = \frac{(x - x_{1}) (x - x_{2}) (x - x_{3})}{(x_{0} - x_{1}) (x_{0} - x_{2}) (x_{0} - x_{3})} L_{0} (4) = \frac{(4 - 5) (4 - 7) (4 - 8)}{(2 - 5) (2 - 7) (2 - 8)} L_{0} (4) = \frac{(- 1) (- 3) (- 4)}{(- 3) (- 5) (- 6)} L_{0} (4) = \frac{2}{15}$

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