A clamped cubic spline S that approximates a function f on [1,3] is defined by : (2 + ²/(x-1) + a(x - 1)³ for x € [1,2] = (3 + b(x-2) + c(x - 2)² + d(x-2)³ for x = [2,3] Given that f'(1) = f'(3), the values of a, b, c and d are respectively: S(x) a = 1/4, b = 3/2, c = 3/4 and d=-3/4. O None of the choices a = 3/4, b = 3/2, c = 3/4 and d=-1/4. O a = 1/4, b = 3/2, c = 3/4 and d=-1/4.
A clamped cubic spline S that approximates a function f on [1,3] is defined by : (2 + ²/(x-1) + a(x - 1)³ for x € [1,2] = (3 + b(x-2) + c(x - 2)² + d(x-2)³ for x = [2,3] Given that f'(1) = f'(3), the values of a, b, c and d are respectively: S(x) a = 1/4, b = 3/2, c = 3/4 and d=-3/4. O None of the choices a = 3/4, b = 3/2, c = 3/4 and d=-1/4. O a = 1/4, b = 3/2, c = 3/4 and d=-1/4.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![A clamped cubic spline S that approximates a function f on [1,3] is defined by:
(2 + ²(x − 1) + a(x - 1)³
for x = [1,2]
(3 + b(x-2) + c(x - 2)² + d(x-2)³ for x € [2,3]
Given that f'(1) = f'(3), the values of a, b, c and d are respectively:
S(x) =
a = 1/4, b = 3/2, c = 3/4 and d=-3/4.
O None of the choices
O a = 3/4, b = 3/2, c = 3/4 and d=-1/4.
O a = 1/4, b = 3/2, c = 3/4 and d=-1/4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F295f3c4b-727e-48e5-afa3-bb9a783a52db%2Fa2fc489d-db4d-4a9a-b04b-a5e440ff5cc3%2Ft2mc9mp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A clamped cubic spline S that approximates a function f on [1,3] is defined by:
(2 + ²(x − 1) + a(x - 1)³
for x = [1,2]
(3 + b(x-2) + c(x - 2)² + d(x-2)³ for x € [2,3]
Given that f'(1) = f'(3), the values of a, b, c and d are respectively:
S(x) =
a = 1/4, b = 3/2, c = 3/4 and d=-3/4.
O None of the choices
O a = 3/4, b = 3/2, c = 3/4 and d=-1/4.
O a = 1/4, b = 3/2, c = 3/4 and d=-1/4.
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