Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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Q2 Let f(x) = 2x3 – 0.0064x2 – 1.5x + 6 (a) Indicate that f(x) = 0 has a root in the interval [-3, 0] with |bo – aol = 1. (b) Examine which method is less iteration (i) to find the root in Q2 (a) by using Secant and Newton-Raphson method. Stop iteration if |f(x)| < 0.0005 or i > 7.
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Transcribed Image Text:Q2 Let f(x) = 2x3 – 0.0064x2 – 1.5x + 6 (a) Indicate that f(x) = 0 has a root in the interval [-3, 0] with |bo – aol = 1. (b) Examine which method is less iteration (i) to find the root in Q2 (a) by using Secant and Newton-Raphson method. Stop iteration if |f(x)| < 0.0005 or i > 7.
LIST OF FORMULA a, +b, i = 0,1,2,... 2 Bisection method: Secant method: Xi+2 , i = 0,1,2 .. f(xi+1) - f(x) ..... Newton-Raphson method: x = x, f(x,) .i = 0,1,2.... f"(x,) f.0 = fi,i = 0,1,..n fU-1] - fj-1 Newton's interpolation: %3D j = 1,2,..,n %3D Xi+j - Xị P,(x) = f0 + f"(x-x)+ f"(x-x, )(x- x)++f"(x-x, )(x-).-(x-x) Lagrange interpolation: P,(x) = L,(x)f, for k 0,1,2,3,.,n with L(x)= -*,) 1-6 (x, -x) i=0
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Transcribed Image Text:LIST OF FORMULA a, +b, i = 0,1,2,... 2 Bisection method: Secant method: Xi+2 , i = 0,1,2 .. f(xi+1) - f(x) ..... Newton-Raphson method: x = x, f(x,) .i = 0,1,2.... f"(x,) f.0 = fi,i = 0,1,..n fU-1] - fj-1 Newton's interpolation: %3D j = 1,2,..,n %3D Xi+j - Xị P,(x) = f0 + f"(x-x)+ f"(x-x, )(x- x)++f"(x-x, )(x-).-(x-x) Lagrange interpolation: P,(x) = L,(x)f, for k 0,1,2,3,.,n with L(x)= -*,) 1-6 (x, -x) i=0
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