For example 1, how did they get 2X^3 - 1 in the numerator? currentnewapproximation approximationfunction f. This step is repeated forn = 0, 1, 2, . . . , until a termination condition is met2 he discussed).We have derived the general step of Newton's method for approximating roots of aNewton's Method for Approximating Roots of f(x) 0FASCED UREChouse an initial approximation x as close to a root as possible.01, 2,. .f(x,)f' (x,)пprovided f'(x) 0.3. End the calculations when a termination condition is met.QUICK CHECK 1 Verify that setting y = 0 in the equation y - f(x, )= f'(x,)(x - xn) andsolving for x gives the formula for Newton's method.Applying Newton's method Approximate the roots off(x)= x-5x + 1 (Figure 4.83) using seven steps of Newton's method. Use4 as initial approximations.EXAMPLE 13X1, and xo-3, xoSOLUTION Noting that f'(x) = 3x-5, Newton's method takes the formf (x,).35x, 112x3пn3x2 -53x2- 5'n+1пnпf'(x,)H0where n 0, 1, 2, ... , and x is specified. With an initial approximation ofe first approximation isХо2(-3)3 13x-5 3(-3)2 -52x01-2.5e second approximation is2x- 1 2(-2.5)3 1-2.345455.2.2

Name: For example 1, how did they get 2X^3 - 1 in the numerator? currentnewa
Uploaded: 2024-03-20T06:46:03.000Z
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Description: For example 1, how did they get 2X^3 - 1 in the numerator? currentnewapproximation approximationfunction f. This step is repeated forn = 0, 1, 2, . . . , until a termination condition is met2 he discussed).We have derived the general step of Newton's