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

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`3cos(x)=x+1`

`f(x)=x+1-3cos(x)=0`

To solve using Newton's method apply the formula,

`x_(n+1)=x_n-f(x_n)/(f'(x_n))`

`f'(x)=1+3sin(x)`

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

`x_(n+1)=x_n-(x_n+1-3cos(x_n))/(1+3sin(x_n))`

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...

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