5 Cubic speine interpolation Hermite spline interpolation :Determine which of the following functions ane*) cuhe speines*) matural cubit splines.+ Which, ay any, of the cubit spline conditions does a given function S(K)met satisty ?a) su) = c) sCx) = Sa(x) = - 4x³-x²+ 2, xEC-107Sz(x) = x3-3x +2, xcco1.d) scx)- Sa(x) x+1)-2x +x+1), xEc107S2(x) - (1-x)3+(1-x) +2x ) x€ ,passing through the pornts [-1,2], Co, [12).Selx) = 2,2-4.87x+ 3,2x² -0,53×?S(X) =FSzcx) = -30,2 +2, 53x- 7, 6x+ 0,67x3SJCK) = 21- 10, 87x+ 2x-0,13xsiK) = x3-2x+1SE= 3x3-x-2x+1, xEC O114) sx) =.%3!S3) =x3+ xa» KECAI2 passibng thsough [-412]salx) = 1 +x+*+ #*, xeS3(x) =-22. 8+ 3012x-10,8x²+ 1i2x², xE ,imerpolating the function t: :11219) scx) =%3Ba) s(x) = Cubic spline interpolation tlermite speine interpolation:Determine whu'ch of the following functions are13i) cuhic speinesit) Matural cubit splines.+ Wuch, af any, of the cubit spline conditions does a given function S(*)mot satisfy?a)sa(x) = 6-6 x+ x°-x+ , xECo11SZCK) = 8- 12x+6x²-x³, xE .S(X) =く[Ans. ) no ir)no]) sx) = くSalx) %= 4+xーx3,KECO1イSzx) = 4+ 7x-6x2+x3, XEC12. [Ans. t) no ir) mo]Sz(x) = Źx3- 2, xECo1. LAns. 1) yes 22) yes]Sa(x) - 3x+イ)~2xt\xt),×EC-イ10c) S(x) = c) S(X)%3D%3Dd) scx)= (Salx) = Cx+1)-2x+ (x+1), xEc-1I07S2(×) = (イーx)?+ま(1ーメ)+2K) XE,passing through the pornts [-112], [o113, [112] [Ans. 1) yes r) yes]

Question

5 Cubic speine interpolation Hermite spline interpolation :Determine which of the following functions ane*) cuhe speines*) matural cubit splines.+ Which, ay any, of the cubit spline conditions does a given function S(K)met satisty ?a) su) = < $1(*) = 6- 6 x+ x-x* , xECo14)- 8- 42x+ 6x-x?, xE<12> .+) scx) = Salx) = 4+x-x3, xE Co14>c) sCx) = Sa(x) = - 4x³-x²+ 2, xEC-107Sz(x) = x3-3x +2, xcco1>.d) scx)- Sa(x) x+1)-2x +x+1), xEc107S2(x) - (1-x)3+(1-x) +2x ) x€ ,passing through the pornts [-1,2], Co, [12).Selx) = 2,2-4.87x+ 3,2x² -0,53×?S(X) =FSzcx) = -30,2 +2, 53x- 7, 6x+ 0,67x3SJCK) = 21- 10, 87x+ 2x-0,13xsiK) = x3-2x+1SE= 3x3-x-2x+1, xEC O11>4) sx) =.%3!S3) =x3+ xa» KECAI2> > passibng thsough [-412]salx) = 1 +x+*+ #*, xe<107Szcx) = 1+x + -x, xe ) = -+ * x - 2 x+ x xe< 412)passing through the pornts [-1,2), [o1), [1,2), [2103.S4 (x) = 0,2x+ 0,8x3 , XE CO11>SzCx) = 218- 8.2x+ 84x2- 2x² , xEC412>S3(x) =-22. 8+ 3012x-10,8x²+ 1i2x², xE<243> ,imerpolating the function t: :11219) scx) =%3Ba) s(x) = Cubic spline interpolation tlermite speine interpolation:Determine whu'ch of the following functions are13i) cuhic speinesit) Matural cubit splines.+ Wuch, af any, of the cubit spline conditions does a given function S(*)mot satisfy?a)sa(x) = 6-6 x+ x°-x+ , xECo11>SZCK) = 8- 12x+6x²-x³, xE <112>.S(X) =く[Ans. ) no ir)no]) sx) = くSalx) %= 4+xーx3,KECO1イ>Szx) = 4+ 7x-6x2+x3, XEC12>. [Ans. t) no ir) mo]Sz(x) = Źx3- 2, xECo1>. LAns. 1) yes 22) yes]Sa(x) - 3x+イ)~2xt\xt),×EC-イ10>c) S(x) = c) S(X)%3D%3Dd) scx)= (Salx) = Cx+1)-2x+ (x+1), xEc-1I07S2(×) = (イーx)?+ま(1ーメ)+2K) XE,passing through the pornts [-112], [o113, [112] [Ans. 1) yes r) yes]

Accepted Answer

Answered: Image /qna-images/answer/ccda3b5f-0035-4143-8466-b8f122d3f62c.jpg

Salx) = 212-4.87x+ 3,2x² -0,53x3 S(K) =FSzcx) = -30,2 +27 53 x- , 6x+ 0,69X, S(x) = 2イ- 40,争K+ Zx-013x? x3-2x+1 *kそく4> A con salx) =