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Question The iteration x[n+1]=( x[n] (x[n]^2 + 3a) ) / (3x[n]^2 + a), is a third order method for computing sqrt(a). Show that: lim n-> inf { ( x[n+1] – sqrt(a) ) / ( x[n] – sqrt(a) )^3 } is bounded.

Question

The iteration x[n+1]=( x[n] (x[n]^2 + 3a) ) / (3x[n]^2 + a),is a third order method for computing sqrt(a).

Show that:

lim n-> inf { ( x[n+1] – sqrt(a) ) / ( x[n] – sqrt(a) )^3 }

is bounded.

 
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