1)10 3f(x)36.211Find the value of x for y=5 using divided differences table for the data.

We have : xk 1 2 0 3 fxk 3 6 2 11 This can be written as: xk x0=0 x1=1 x2=2 x3=3 fxk…

Answered: 1) 1 3 f(x,) 3 6 11 Find the value of x…

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

1)
1
0 3
f(x)
3
6.
2
11
Find the value of x for y=5 using divided differences table for the data.

Expert Solution

Step 1

We have :

$x_{k}$	1	2	0	3
$f (x_{k})$	3	6	2	11

This can be written as:

$x_{k}$	$x_{0} = 0$	$x_{1} = 1$	$x_{2} = 2$	$x_{3} = 3$
$f (x_{k})$	$f (x_{0}) = 2$	$f (x_{1}) = 3$	$f (x_{2}) = 6$	$f (x_{3}) = 11$

Now, the formula for the divided difference is:

$y = f (x) = f (x_{0}) + (x - x_{0}) f [x_{0,} x_{1}] + (x - x_{0}) (x - x_{1}) f [x_{0,} x_{1}, x_{2}] + (x - x_{0}) (x - x_{1}) (x - x_{2}) f [x_{0,} x_{1}, x_{2}, x_{3}]$

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