Explanation Procedure used: Procedure Newton’s Method for Approximating Roots of f ( x ) = 0 : 1 Choose an initial approximation x 0 as close to a root as possible. 2 For n = 0 , 1 , 2 , ... , x n + 1 = x n − f ( x n ) f ′ ( x n ) , provided f ′ ( x n ) ≠ 0 . 3 End the calculations when a termination condition is met. Calculation: The given function is f ( x ) = tan x − 2 x with initial condition x 0 = 1.2 . Differentiate f ( x ) = tan x − 2 x with respect to x on both sides as follows. d d x ( f ( x ) ) = d d x ( tan x − 2 x ) f ′ ( x ) = sec 2 x − 2 Newton’s method takes the form x n + 1 = x n − tan x n − 2 x n sec 2 x n − 2 . Where n = 0 , 1 , 2 , ... and x 0 is specified with an initial approximation x 0 = 1

Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

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ISBN: 9780134996714

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 4.8, Problem 17E

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To approximate: A root of f(x)=tanx−2x using Newton’s method.

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Chapter 4.8, Problem 16E

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Chapter 4 Solutions

Calculus: Single Variable, Early Transcendentals and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition) (Briggs, Cochran, Gillett & Schulz, Calculus Series)

Ch. 4.1 - Sketch the graph of a function that is continuous...Ch. 4.1 - Consider the function f(x) = x3. Where is the...Ch. 4.1 - Sketch the graph of a function that is continuous...Ch. 4.1 - Sketch the graph of a function that has an...Ch. 4.1 - What is a critical point of a function?Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Prob. 12E Ch. 4.1 - Absolute maximum/minimum values Use the following...

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To approximate: A root of f ( x ) = tan x − 2 x using Newton’s method.

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