subject :Advance mathematics

Steps:

1.Find points a and b such that a

4. Then use the formula: x1 = x0- (f (x0) / f' (x0))

5. If f (x1) = 0, then x1 is an exact root, else x0 = x1.

6. Repeat steps 3 to 5 until f(xi) = 0 or |f(xi)| ? Accuracy

(CONVERGENCE)

Example problem:

EXAMPLE 1 ( a ) x f (b ) 20 Find a root of an equation f(x) = x3- x -1 using Newton Raphson method. f( x ) = X" - X - 1 to = atb 71 = XD- f (x f ( x ) = 3 2 - a b X /D = 15 01875 2 4 (x)1 -1 - XP = 15 5.75 S 2 f ( 1 5 ) = 0. 875 X1 = 1,3478 + (1 15 ) = 5.75of (x ) = 3x - 1 EXAMPLE 1 Find a root of an equation f(x) = x3- x - 1 using Newton Raphson method. X- 13478 $ (1,3252 ) = 0.002 f ( 1 : 3478 ) = 0. 1006 f ( 1. 3252 ) = 4, 2685 X3 = 1. 3247 f ( 1 : 3478) - 4. 4 497 *3 = 1:3252 - 0.0021 X2= 13478 0100 6 A.2485 4 44 97 Xz = 1:3247 - 13252 - 0.000 08 f ( 1 3247 7 0. 75481. Find a root of an equation f(x) = 2x3 - 2x - 5 using Newton Raphson method. 2. Find a root of an equation f(x)=31/48 (cube root of 48) using Newton Raphson method. 3. Find a root of an equation f(x) = x3 + 2x2 + x - 1 using Newton Raphson method