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Alpha=9 beta=3 yazarsin 2. ( 20p.) Consider the cubic spline for a function f on (0,2)...
beta is 1 2. ( 20p.) Consider the cubic spline for a function f on (0, 2) defined by 223 + ax2 + rx + 1 if 0 < x < 1 S(X) = (.x - 1)3 + c(x - 1)2 + d(x - 1) + B if i < x < 2 S(x) = { where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
2. Consider the cubic spline for a function f on [0, 2] defined by S(x) = { ={ (z. 2x3 + ax2 + rx +1 if 0 < x <1 (x - 1)3 + c(x - 1)2 + d(x - 1) + ß if 1 < x < 2 where r, c and d are constants. Find f'(0) and f'(2), if it is a clamped cubic spline.
alpha = 3 beta =2 Can you solve it in a hour please Thank you very much. 2. (20p.) Consider the cubic spline for a function f on (0,2] defined by S(z) = { (-- 1)327 ct an 10 Fritisa52 where r,c and d are constants. Find f'O) and f'(2), if it is a clamped cubic spline.
Numerical analysis Question 1 A clamped cubic spline Six) on interval [0, 2) is defined by S(x) - 3 + ax + bx2 - 2x06x<1 (3 + c(x - 1) - 4(x - 1)2 + 7(x - 1) 1sx52 where a, b, care constants. Find the values of S'(0) and S(2).
Homework Problem Set 16 x-1)3 for 0 sx$1 a cubic spline? 1. Is the function s (x) = {2(-1)3 for 1 < x 2 -5 +8x-6x2 2x3 for1 sx s 2 Is the function s(x)-[ natural? Let x for j 1,2,3,4 by a calculation on paper 3 a cubic spline? Is it [1,0,1,0]. Determine the natural spline s with s(y)-yi 2. 18x2-2x3 for 2
Define the following functions, and verify if cubic splie on given interval, also determine if natural spline. on al Define: Sx) = -5+86-66x² + 2x3 12XL 2 land S(x) = 27-40x +18% - 2x² on. 22X<3 b) Verify that Sx) is a cubic spline function on 6 Is it a natural spline function on this interual?
Linear Algebra A natural cubic spline for a function f(x) is defined by ſax° +15x² – 21.75x +14.5 15x521 S(x) = ayx? + 3x² + 2.25x-1.5 25 x 3] Find the value of a1.
Q8 Spline 15 Points Define s(2) = -5 + 8x6x2 + 2x2 on 1 < x <2, and 8(x) = 27 402 + 1822. on 2<< <3 Verify that s() is a cubic spline function on (1,3). Is it a natural spline function on this interval?
2. A natural cubic spline S is defined by S(z) = { $(") = 11 S. (C)=1+ B(-1) + D(x - 1)3 S (2)=1+b(-2) + 3(x - 2)2 + (x - 2) if 1 <3 <2 if 2 <3<3 Find B, D, b, and d. Hint: Recall that a natural cubic spline has S" equal to 0 at the endpoints.
It is known that f :(0,2) + R is a differentiable function such that \f'(x) < 5 for all x € (0,2). Now let bn := f(2 – †) for all n € N. Prove that this is a Cauchy sequence.