Question

The third forward difference Ayo-.............
Options
о уз-уо
O -
Y3-Y2+yı-Yo
O Y3-3y2+3y1-Yo
O Y3-3yı​

Answer 1

Answer:

Hey dude

Step-by-step explanation:

Thanks for free points

Answer 2

Answer:

The third forward difference is $\Delta^3y_n=\Delta^{2}y_{n+1}-\Delta^{2}y_n$

Step-by-step explanation:

As the mathematical expressions are not clear, the answer is given considering only the text given, that is third forward difference.

The forward difference of a function $y_{n}$ is given by

                     $\Delta y_n=y_{n+1}-y_n$

and repeatedly using the forward difference operator, the higher order differences are obtained. Generalizing to $k^{th}$ time

                              $\Delta^ky_n=\Delta^{k-1}y_{n+1}-\Delta^{k-1}y_n$

Therefore the third forward difference is given by, using $k=3$ in the above equation

                         $\Delta^3y_n=\Delta^{3-1}y_{n+1}-\Delta^{3-1}y_n$

                         $\Delta^3y_n=\Delta^{2}y_{n+1}-\Delta^{2}y_n$  

The third forward difference is $\Delta^3y_n=\Delta^{2}y_{n+1}-\Delta^{2}y_n$