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# Use Newton's method to approximate the indicated root of the equation correct to six decimal places.The positive root of $3\sin x = x$

## 2.278863

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In order to perform Newton's method, we need to have the derivative, which is gonna be one minus three coast Xanax. We can estimate x one to be 2.1. So initial approximation, therefore, X to repeating the process 2.1. Let us off with 2.1 over Russell F Prime of 2.1. This is 2.29 now x three. Using Newton's method again, it's gonna be 2.27 Axe four was gonna be 2.27 x five is gonna be 2.27 Therefore, axe is gonna be 2.27 a 63 with all the decimals that we can, right?

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