Question

If xe = 10, h = 10,yo = 9,8yo = 30,Ayo = 5,4'yo = 2, then the value of
f(15) obtained from given data by Newton Gregory forward interpolation formula​

Answer 1

Answer:

answer is 1⁰0⁰⁰⁰⁰⁰0⁰⁰⁰00⁰

Answer 2

Answer:

Value of f(15)=23.5

Step-by-step explanation:

Given $x_{0} = 10$, $h = 10$, $y_{0} =9$

Assuming the given data is $\Delta y_{0} =30$, $\Delta^{2} y_{0} =5$, $\Delta^{3} y_{0} =2$

From $f(15), x=15$

Therefore, $x_{0} +nh=15 \implies 10 +n\times 10=15\implies n=0.5$

Newton Gregory forward interpolation formula​ is given by

$y_{x} =y_{0}+n \Delta y_{0}+\frac{n(n-1)}{2!} \Delta^{2} y_{0}+\frac{n(n-1)(n-2)}{3!} \Delta^{3} y_{0}+...$      

$y_{15} =9+0.5 \times 30+\frac{0.5(0.5-1)}{2} \times 5+\frac{0.5(0.5-1)(0.5-2)}{6} \times2$

     $=9+15-0.625+0.125=23.5$