The formula for the secant method is given below. Xn - 1- Xn - 2 F(x-1)-(x, - 2) X, = Xn -1- f(x, - 1) Use both Newton's method and the secant method, given above, to calculate a root for the following equation, f(x). Use a calculator or computer to calculate how many iterations of each are needed to reach within three decimal places of the exact answer. For the secant method, use the first guess from Newton's method. f(x) - x2 + 14x + 49, x,- 1 Newton's method iterations

The formula for the secant method is given below. Xn - 1- Xn - 2 F(x-1)-(x, - 2) X, = Xn -1- f(x, - 1) Use both Newton's method and the secant method, given above, to calculate a root for the following equation, f(x). Use a calculator or computer to calculate how many iterations of each are needed to reach within three decimal places of the exact answer. For the secant method, use the first guess from Newton's method. f(x) - x2 + 14x + 49, x,- 1 Newton's method iterations

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

The formula for the secant method is given below.
Xn - 1- Xn - 2
Xn = Xn - 1- f(xn - 1)-
f(x, - 1) - f(xn – 2)
Use both Newton's method and the secant method, given above, to calculate a root for the following equation, f(x). Use a calculator or computer to calculate how many iterations of each are needed to reach
within three decimal places of the exact answer. For the secant method, use the first guess from Newton's method.
f(x) = x2 + 14x + 49, x, = 1
Newton's method
iterations
secant method
iterations

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