Explanation Given: The function is f ( x ) = cos x − 4 x , x 0 = 1 . Formula used: Newton method: x n + 1 = x n − f ( x n ) f ′ ( x n ) Calculation: The function is f ( x ) = cos x − 4 x , x 0 = 1 . We have to find the value of x 1 , x 2 and x 3 . Find the derivative of function. f ′ ( x ) = − sin x − 4 Use the formula: x n + 1 = x n − f ( x n ) f ′ ( x n ) Compute the successive approximations. First, find the value of x 1 . x 1 = x 0 − f ( x 0 ) f ′ ( x 0 ) = x 0 − cos x 0 − 4 x 0 − sin x 0 − 4 Substitute − 1 for x 0 in the above function. x 1 = 1 − cos ( 1 ) − 4 ( 1 ) − sin ( 1 ) − 4 = 1 + cos ( 1 ) − 4 ( 1 ) sin ( 1 ) + 4 = 1 − 3.4596976 4.8414709 = 0.2854 Now, find the value of x 2

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ISBN: 9781319434526

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 4.7, Problem 5E

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Use Newton method to f and initial guess x0 to find x1,x2 and x3.

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Chapter 4.7, Problem 4E

Chapter 4.7, Problem 6E

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Chapter 4 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

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Use Newton method to f and initial guess x 0 to find x 1 , x 2 and x 3 .

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Chapter 4 Solutions