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Construct the natural cubic spline for the following data

28/04/2021 Client: muhammad11 Deadline: 2 Day

Construct the natural cubic spline for the following data.
a.
x 
f(x) 
0 
1.00000 
0.5 
2.71825 
b.
x 
f(x) 
-0.25 
1.33203 
0.25 
0.800781 
c.
x 
f(x) 
0.1 
-−0.29004996 
0.2 
−0.56079734 
0.3 
−0.81401972 
d.
x 
f(x) 
-1 
0.86199480 
0.5 
0.95802009 
0 
1.0986123 
0.5 
1.2943767 
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Find and graph the natural cubic spline interpolant for the following data:a. b. c. d.
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a. Use Algorithm 3.2 to construct the interpolating polynomial of degree three for the unequally spaced points given in the following table: x f (x) ?0.1 5.30000 0.0 2.00000 0.2 3.19000 0.3 1.00000 b. Add f (0.35) = 0.97260 to the table, and construct the interpolating polynomial of degree...
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Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate...... c. f (0.18) if f (0.1) = ?0.29004986, f (0.2) = ?0.56079734, f (0.3) = ?0.81401972, f (0.4) = ?1.0526302 d. f (0.25) if f (?1) = 0.86199480, f (?0.5) = 0.95802009, f (0) = 1.0986123, f...
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Use Neville\'s method to obtain the approximations for Lagrange interpolating polynomials of...... c. f (0.18) if f (0.1) = ?0.29004986, f (0.2) = ?0.56079734, f (0.3) = ?0.81401972, f (0.4) = ?1.0526302 d. f (0.25) if f (?1) = 0.86199480, f (?0.5) = 0.95802009, f (0) = 1.0986123, f...
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