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posted by  Novaworks on 11/3/2009 3:03:03 PM  |  status: Closed  |  Earned Karma: 1145

Newton's method to indicated the root...

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Calculus N/A N/A N/A 11/4/2009 at 8:00:00 PM
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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 2cos(x) = x3
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posted by Paul K on 11/3/2009 4:14:11 PM  |  status: Live
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Question Details:
Use Newton's method to approximate the indicated root of the equation correct to six decimal places.
The positive root of 2cos(x) = x3
     . Putting this in the form  , we get :
 . Take the derivative of this , and you get :
. The iteration formula that gives successively better approximations given an initial
quess is :
.  Start with  ( your calculator must be in radian mode ) , and you get :
.
Notice that the numerator of the fraction , which is  ,  is getting closer and closer to zero .If we continue in this manner,
we will get to eleven decimal places :
. We thus have to  decimal places :
.
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