Question

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.

Answer 1

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

Answer 2

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

Answer 3

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}

Answer 4

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

Answer 5

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)