Find c in the following cubic splines. Which of the three end conditions—natural, parabolically terminated, or not-a-knot—if any, are satisfied? S ( x ) = { 4 − 11 4 x + 3 4 x 3 on [ 0 , 1 ] 2 − 1 2 ( x − 1 ) + c ( x − 1 ) 2 + 3 4 ( x − 1 ) 3 on [ 1 , 2 ] S ( x ) = { 3 − 9 x + 4 x 2 on [ 0 , 1 ] − 2 − ( x − 1 ) + c ( x − 1 ) 2 on [ 1 , 2 ] S ( x ) = { − 1 + c ( x − 1 ) + 1 2 ( x − 1 ) 2 − ( x − 1 ) 3 on [ 1 , 2 ] 1 + 1 2 ( x − 2 ) − 5 2 ( x − 2 ) 2 − ( x − 2 ) 3 on [ 2 , 3 ]
Find c in the following cubic splines. Which of the three end conditions—natural, parabolically terminated, or not-a-knot—if any, are satisfied? S ( x ) = { 4 − 11 4 x + 3 4 x 3 on [ 0 , 1 ] 2 − 1 2 ( x − 1 ) + c ( x − 1 ) 2 + 3 4 ( x − 1 ) 3 on [ 1 , 2 ] S ( x ) = { 3 − 9 x + 4 x 2 on [ 0 , 1 ] − 2 − ( x − 1 ) + c ( x − 1 ) 2 on [ 1 , 2 ] S ( x ) = { − 1 + c ( x − 1 ) + 1 2 ( x − 1 ) 2 − ( x − 1 ) 3 on [ 1 , 2 ] 1 + 1 2 ( x − 2 ) − 5 2 ( x − 2 ) 2 − ( x − 2 ) 3 on [ 2 , 3 ]
Solution Summary: The author explains that Tio find the c in the cubic spline and which condition is satisfied for S(x)= leftl4-
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY