## butalier 4 years ago use newtons method to approximate a real zero of f(x)=x^2-11, accurate to 4 decimal places. start with 3.2. do 2 iterations. show the entire table.

1. aama100

ANSWER: 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

2. aama100

ignore the last two lines .. I pasted them by a mistake

3. aama100

ANSWER: 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}

4. butalier

what is the meaning of iteration and how to show the table?

5. aama100

to 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)