The quadratic term in a Taylor series expansion of f can be used to define a moreaccurate x1from x, . This means we define x as the root of the quadratic'n+10 = f(x,)+(x- x,)f'(x,)+÷(x-1-x,)/"(x,).This leads to the iteration2f(x,)f'(x,)± [S"(x, )]– 2f(x,)f"(x,)'Xp+1 = x,where we choose the sign in the denominator to make x,1 closer to x,, i.e., to maximisen+1the magnitude of the denominator.Define f(x) = x –-5. Use EXCEL and apply this method to find an estimation for 5correct to four decimal places. Start with x, = 2.

The given function is, f(x)=x2-5. The derivatives are, f'(x)=2x and f''(x)=2 . Initial value of x is…

The quadratic term in a Taylor series expansion of f can be used to define a more accurate x from x,. This means we define x as the root of the quadratic 0= f(x,) + (x – x,)f'(x,)+(x -x,)S"(x,). This leads to the iteration 2f(x,) f'(x,) ± IS"(x,)]– 2f(x, )S"(x,) where we choose the sign in the denominator to make x, closer to x,, i.e., to maximise X+1 = x, 'n+1 the magnitude of the denominator. Define f(x) = x² - 5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.

The quadratic term in a Taylor series expansion of f can be used to define a more accurate x from x,. This means we define x as the root of the quadratic 0= f(x,) + (x – x,)f'(x,)+(x -x,)S"(x,). This leads to the iteration 2f(x,) f'(x,) ± IS"(x,)]– 2f(x, )S"(x,) where we choose the sign in the denominator to make x, closer to x,, i.e., to maximise X+1 = x, 'n+1 the magnitude of the denominator. Define f(x) = x² - 5. Use EXCEL and apply this method to find an estimation for 5 correct to four decimal places. Start with x, = 2.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter1: Fundamental Concepts Of Algebra

Section1.3: Algebraic Expressions

Problem 5E

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