`3cos(x) = x + 1` Use Newton's method to find all roots of the equation correct to six decimal places.

Textbook Question

Chapter 4, 4.8 - Problem 17 - Calculus: Early Transcendentals (7th Edition, James Stewart).
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gsarora17 | (Level 2) Associate Educator

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To solve using Newton's method apply the formula,



Plug in f(x) and f'(x) in the formula,


See the attached graph to get the initial values of x.

When f(x)=0 , the values of x are near The curve has three x values x `~~` 0.8 , -1.8 , -3.6

Use these three values for finding the roots of the equation to six decimal places.

Let's solve for the first zero by initial value  x_1=0.8






Let's stop iteration as we have same decimal places

Now let's solve for the second zero by initial value x_1=-1.8,






Now let's solve for the third root by initial value x_1=-3.6






Roots of the equation to six decimal places are 0.889470 , -1.862365 , -3.637958

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