$1.00 Newton's Method
f(x)=x^5-2x^4+x^3-x^2+2x-3 has a root near 1. Letting x =2 be the first approximation to a root, use Newton's Method to compute the second and third approximations. This third approximation is accurate to how many decimal places? Explain your reasoning.
Computing with Newton's Method - Accuracy of Approximation
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- Posted on Apr 09, 2009 at 4:16:21PM
Preview: ... rly 1.70836.<br><br>So our 3rd approximation has 2 digits correct. Let's see if we can justify that another way.<br><br>We're told that the root is near 1. So we'll interpret that to be that the first digit is 1. Notice that the first approximation has no digits correct. The second approximation has 1 as the first digit, so it agrees to 1 digit ...
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