1. Calculate f(1.5), f(4.5), f(7.5) using newton interpolation method from the following data:
x : 1, 2, 3, 4, 5, 6, 7, 8 f(x) : 1, 8, 27, 64, 125, 216, 343, 512
2. Calculate f(1.6), f(2.4), f(2.8) from the following data using newton interpolation:
x : 1.0 ,1.5, 2.0, 2.5 ,3.0 f(x) : 0.11246, 0.14032, 0.16800, 0.19547, 0.22270
3.Calculate f(0.33), f(0.39) from the following data using newton interpolation:
x : 0.30, 0.32 ,0.34, 0.36, 0.38 ,0.40 f(x) : 1.7596 ,1.7698 ,1.7804, 1.7912 ,1.8024 ,1.8139
1.(a) Calculate f(1.5), f(4.5), f(7.5) from the following data:
x : 1 2 3 4 5 6 7 8 f(x) : 1 8 27 64 125 216 343 512
(b) Calculate f(1.6), f(2.4), f(2.8) from the following data:
x : 1.0 f(x) : 0.11246
1.5 0.14032
2.0 0.16800
2.5 0.19547
3.0
0.22270
(c) Calculate f(0.33), f(0.39) from the following data:
x : 0.30 0.32 0.34 0.36 f(x) : 1.7596 1.7698 1.7804 1.7912
0.38 1.8024
0.40 1.8139
2.(a) (b) Calculate f'(0.33), f"(0.33), f'(0.39), f"(0.39) from the following data: : 0.30 0.32 0.34 0.36 0.38 f(x) : 1.7596 1.7698 1.7804 1.7912 1.8024
0.40 1.8139
(c) Calculate f'(0.8), f"(0.8), f'(0.82), f"(0.82) from the following data:
X : 0.4 f(x) :. 1.08107
0.6 1.18546
0.8 1.33743
1.0 1.54308
1.2 1.81066