Let a be a fixed number with > 0.

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You are using Newton's method with deflation to find the roots

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Numerical Analysis : Newton's Method : Sequence Convergence : Multiplicity

Problem Attached. Please site any Theorems used. Thank you very much.

Numerical Analysis : Sequence Convergence & Limit Proof

Suppose {p_n} converges to p. Prove that there is at most one alpha for which the limit as n goes to infinity of |p_n+1-p|/(|p_n-p|^alpha) is a positive finite number. (See attachment for mathematical notation)

Kinky Copies may buy a high-volume copier.

Please help me determine the solution as to why or why not Kinky should buy the machine. Break it down for me so I would have a clear understanding. Project evaluation. Kinky Copies may buy a high-volume copier. The machine cost $100,000 and will be depreciated straight-line over 5 years to a salvage value of $20,000. Kinky anticipates that the machine actually can be sold in 5 years for 30,000. The machine will save $20,000 a year in labor costs but will require an increase in working capital, mainly paper supplies, of $10,000. The firms marginal tax rate is 35 percent, and the discount rate is 8 percent. Should Kinky buy the machine.