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Question: How do I derive a recurrence relations

Question:How do I derive a recurrence relations

ETM1697 10
calculus multivariate
October 27 2016
1


equation 1 : xi+1=xi− (f·gy−fy·g)/(fx ·gy −fy ·gx)
equation 2: yi+1=yi− (fx·g−f·gx)/(fx·gy-fy·gx)

My quesiton are, deriving equations (1) and (2) above and constructing a single Maple function called newt2d that implements both of these recurrence relation.

I apolgize in advance if I don't write my question correctly.  This is my first time posting a question. 
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