Question

If x = 1961, h = 10. yn = 101. Vy, = 8.v2x, = -4.V'y,
= -1.V'y, = -3
then the value of f(1955) obtained from given data by using Newton Gregory
backward interpolation formula is​

Answer 1

Answer:

The value of f(1955) is 5.132

Step-by-step explanation:

Given, $x = 1961$, $h = 10$

And assuming other other values could be $y_{0} = 8$, $\Delta y_{0} = -4$, $\Delta^{2} y_{0} = -1$, $\Delta^{3} y_{0} = -3$

Given $x_{0}=1955$,  

so, from $x=x_{0} +nh\implies 1961=1955 +n\times 10$    

                                   $\implies n=\frac{1961-1955}{10}=0.6$

Using Newton Gregory forward interpolation formula​ is given by

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

$y_{1955} =8+0.6\times (-4)-\frac{0.6(0.6-1)}{2}-\frac{0.6(0.6-1)(0.6-2)}{6!}\times 3$          

        $=8-2.4-0.12-0.168=5.132$