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Numerade Educator

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Problem 17 Medium Difficulty

Use Newton's method to find all solutions of the equation correct to six decimal places.

$ 3\cos x = x + 1 $

Answer

$x \approx-3.637958,-1.862365,0.889470$

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Martin B.

April 8, 2020

Could you please take the time to explain how you got the initial value of x?

Video Transcript

Okay. We know we take the derivative, which is F Prime of X is negative. One minus three side of X. We know ex of one is negative. 3.7. This could be our initial approximation. Then we know exits to plugging into Newton's formula. We get negative. 3.63 we know except three is negative. 3.63 And except for his negative 3.63 acts of five repeating the same processes negative. 3.63 which gives us X is approx more negative. 3.63 7957 We could do the same process with extra ones. Negative. 1.9 we get. AKs is 1.8. Sex acts of one is one. We access approximately zero point a nine 470