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Question

(D) To find $\Delta^{5} u_{x}$,we construct the forward difference table:

	
		
			$x, u_{x}$
			$\Delta u_{x}, \Delta^{2} u_{x}, \Delta^{3} u_{x

Vedclass · Accepted Answer

$755$

Vedclass · Answer

(D) To find $\Delta^{5} u_{x}$,we construct the forward difference table:

	
		
			$x, u_{x}$
			$\Delta u_{x}, \Delta^{2} u_{x}, \Delta^{3} u_{x}, \Delta^{4} u_{x}, \Delta^{5} u_{x}$
		
		
			$0, 3$
			$9, 60, -10, -259, 755$
		
		
			$1, 12$
			$69, 50, -269, 496$
		
		
			$2, 81$
			$119, -219, 227$
		
		
			$3, 200$
			$-100, 8$
		
		
			$4, 100$
			$-92$
		
		
			$5, 8$
			-
		
	


The forward difference $\Delta^{5} u_{0}$ is calculated as follows:
$\Delta u_{0} = u_{1} - u_{0} = 12 - 3 = 9$
$\Delta u_{1} = u_{2} - u_{1} = 81 - 12 = 69$
$\Delta u_{2} = u_{3} - u_{2} = 200 - 81 = 119$
$\Delta u_{3} = u_{4} - u_{3} = 100 - 200 = -100$
$\Delta u_{4} = u_{5} - u_{4} = 8 - 100 = -92$
Continuing this process for higher-order differences,we obtain the final value $\Delta^{5} u_{0} = 755$.

For a certain function $u_{x}$,given that $u_{0}=3, u_{1}=12, u_{2}=81, u_{3}=200, u_{4}=100, u_{5}=8$,then $\Delta^{5} u_{x}$ is equal to

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