For a given function f(x), the divided-differences table is given by: Xo - a -1 f[xo] = 0 S[x] = 2 flxo»x1] = 4b Slx2] = -1 flx,x2] = -1 -a+1 The values of a and b are: a=3 and b=2/3 O a=-2 and b=-1/2 a=3 and b=-1/2 O a=-2 and b=2/3 A natural cubic spline S for a function fis defined by

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
numerical
For a given function f(x), the divided-differences table is given by:
Xo - a - 1
f (xo] = 0
X1 =1
X2 - a +1
S[x1] = 2 flxo, x1] = 4b
S[x2] = -1 S(x1, X2] = -1
The values of a and b are:
a=3 and b=2/3
O a=-2 and b=-1/2
a=3 and b=-1/2
a=-2 and b=2/3
A natural cubic spline S for a function fis defined by
x x2
3
15x< 2
12
4
S(x) =
3x
+ ах +
4
2 < x< 3
3 sx54
12
An approximation of f '(2.75) is:
-0.52083
-0.14825
-0.09895
-0.14583
Transcribed Image Text:For a given function f(x), the divided-differences table is given by: Xo - a - 1 f (xo] = 0 X1 =1 X2 - a +1 S[x1] = 2 flxo, x1] = 4b S[x2] = -1 S(x1, X2] = -1 The values of a and b are: a=3 and b=2/3 O a=-2 and b=-1/2 a=3 and b=-1/2 a=-2 and b=2/3 A natural cubic spline S for a function fis defined by x x2 3 15x< 2 12 4 S(x) = 3x + ах + 4 2 < x< 3 3 sx54 12 An approximation of f '(2.75) is: -0.52083 -0.14825 -0.09895 -0.14583
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,