Newton's Method

Vader07

New member
Joined
Oct 7, 2009
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9
Hello everyone,

Apply Newton's method to find a root of

f(x) = x^3 -7

in the interval (1, 2). If your initial guess is x0 = 2, then approximately
how far is x2 from the cube root of seven (the actual root of the equation)?

This is how I began the problem
Step 1: x - (x^3) -7)/ 3x^2
Step 2: x - (8-7)/ 12
Step 3: 2 - (1/12)
Step 4: 24/12 - 1/12 = 23/12
Step 5: [23/12 - (23/12)^3 - 7] / (3 (23/12)^3)

After step 5 I think I am close to solving it or I am doing this wrong. I have tried to get the answer but I havent come close.
 
Vader07 said:
Hello everyone,

Apply Newton's method to find a root of

f(x) = x^3 -7

in the interval (1, 2). If your initial guess is x0 = 2, then approximately
how far is x2 from the cube root of seven (the actual root of the equation)?

This is how I began the problem
Step 1: x - (x^3) -7)/ 3x^2
Step 2: x - (8-7)/ 12
Step 3: 2 - (1/12)
Step 4: 24/12 - 1/12 = 23/12

Step 5: X[sub:2ufcqm2e]2[/sub:2ufcqm2e] = 23/12 - [ (23/12)^3 - 7] / (3*(23/12)^2)

After step 5 I think I am close to solving it or I am doing this wrong. I have tried to get the answer but I havent come close.

\(\displaystyle ^3\sqrt{7} = 1.912931183\)

What do you get at step 5? Do you not own a calculator?
 
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