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 3 years ago
use newtons method to approximate a real zero of f(x)=x^211, accurate to 4 decimal places. start with 3.2. do 2 iterations. show the entire table.
 3 years ago
use newtons method to approximate a real zero of f(x)=x^211, accurate to 4 decimal places. start with 3.2. do 2 iterations. show the entire table.

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aama100
 3 years ago
Best ResponseYou've already chosen the best response.0ANSWER: f(x) = 11+x^2 f'(x) = 2 x g(x) = x  ( f(x)/f'(x) ) = x(11+x^2)/(2 x) Initial value = 3.2 Number of iteration = 30 The iteration sequence of g(x) : {3.2,3.31875,3.31663,3.31662} It took 3 steps to converge within 0.01 of each other , without counting the initial value of 3.2 The iteration sequence seems to converge to 1

aama100
 3 years ago
Best ResponseYou've already chosen the best response.0ignore the last two lines .. I pasted them by a mistake

aama100
 3 years ago
Best ResponseYou've already chosen the best response.0ANSWER: f(x) = 11+x^2 f'(x) = 2 x g(x) = x  ( f(x)/f'(x) ) = x(11+x^2)/(2 x) Initial value = 3.2 Number of iteration = 2 The iteration sequence of g(x) : {3.2,3.31875,3.31663,3.31662}

butalier
 3 years ago
Best ResponseYou've already chosen the best response.0what is the meaning of iteration and how to show the table?

aama100
 3 years ago
Best ResponseYou've already chosen the best response.0to solve your question you need to the follow procedure : 1) find a g(x) 2) apply g(3.2) , then the result will be applied again g(g(3.2)), and so forth ; this depends on the number of iterations that you want. This will give you a list ( the table)
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