14. Is the following function a cubic spline on [0, 3]? 0< x < 1 1 < x < 2 2

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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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14. Is the following function a cubic spline on [0, 3]?
0 < x < 1
2х — 1,
3x2 - 9,
s(x)
1 < x < 2
2 < x < 3
15.
Define
x³ + 2x2 + 1,
-2x3 + Bx2 - 36x + 25,
1<x < 2
2 < x < 3
s(x)
For a special value of B, s(x) is a cubic spline function on [1, 3]. Find that value
of B and then verify that s(x) is a cubic spline function on [1, 3]. Is it a natural
cubic spline function on this interval?
--..... . ,.·:
. .. ......... ..... ..... .-. -ra.
- . . n . --..- --
Transcribed Image Text:14. Is the following function a cubic spline on [0, 3]? 0 < x < 1 2х — 1, 3x2 - 9, s(x) 1 < x < 2 2 < x < 3 15. Define x³ + 2x2 + 1, -2x3 + Bx2 - 36x + 25, 1<x < 2 2 < x < 3 s(x) For a special value of B, s(x) is a cubic spline function on [1, 3]. Find that value of B and then verify that s(x) is a cubic spline function on [1, 3]. Is it a natural cubic spline function on this interval? --..... . ,.·: . .. ......... ..... ..... .-. -ra. - . . n . --..- --
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