Question 2: A function S is defined on the interval [(-1,3] by S₁(x), x[-1,0), S(x) = S2(x), x[0, 2), S3(2), x = a € [2,3, where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1, where x1 -1, x2 = 0, x3 = 2 and x4 = 3. = 3 11 - If S₁(x) = − ³½³√(x + 1)³ + 2 2 9 (5) (x+1)3 and S3(x) = − 3√(x − 2) ³ + √(x − 2)² + (x − 2) — 3, - use some of the constraints derived above to determine S2(x).
Question 2: A function S is defined on the interval [(-1,3] by S₁(x), x[-1,0), S(x) = S2(x), x[0, 2), S3(2), x = a € [2,3, where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that must be satisfied if S is a natural cubic spline interpolating the function defined by equations f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1, where x1 -1, x2 = 0, x3 = 2 and x4 = 3. = 3 11 - If S₁(x) = − ³½³√(x + 1)³ + 2 2 9 (5) (x+1)3 and S3(x) = − 3√(x − 2) ³ + √(x − 2)² + (x − 2) — 3, - use some of the constraints derived above to determine S2(x).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.3: Zeros Of Polynomials
Problem 3E
Related questions
Question
![Question 2:
A function S is defined on the interval [(-1,3] by
S₁(x),
x[-1,0),
S(x) =
S2(x),
x[0, 2),
S3(2),
x =
a € [2,3,
where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that
must be satisfied if S is a natural cubic spline interpolating the function defined by equations
f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1,
where x1 -1, x2 = 0, x3 = 2 and x4 = 3.
=
3
11
-
If S₁(x) = − ³½³√(x + 1)³ +
2
2
9
(5)
(x+1)3 and S3(x) = − 3√(x − 2) ³ + √(x − 2)² + (x − 2) — 3,
-
use some of the constraints derived above to determine S2(x).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F69cce4ac-4bf6-4e6b-8636-bf160e045b58%2Fc9b37ca6-0546-4c01-9fe2-b7c56b418e1c%2F18iigg_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 2:
A function S is defined on the interval [(-1,3] by
S₁(x),
x[-1,0),
S(x) =
S2(x),
x[0, 2),
S3(2),
x =
a € [2,3,
where S1, S2 and S3 are cubic polynomials. Write down the system of twelve equations that
must be satisfied if S is a natural cubic spline interpolating the function defined by equations
f(x1)=-3, f(x2) = 1 f(x3) = -3 and f(x4) = 1,
where x1 -1, x2 = 0, x3 = 2 and x4 = 3.
=
3
11
-
If S₁(x) = − ³½³√(x + 1)³ +
2
2
9
(5)
(x+1)3 and S3(x) = − 3√(x − 2) ³ + √(x − 2)² + (x − 2) — 3,
-
use some of the constraints derived above to determine S2(x).
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