hw2 - Homework 2 Math 104A Fall 2010 Due on Tuesday October 12th 2010 Section 2.1 6 12 14 16 and 20 Section 2.2 1 2 3 4 11.a 11.b 11.c and 23 Additional

# hw2 - Homework 2 Math 104A Fall 2010 Due on Tuesday October...

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Homework 2 – Math 104A, Fall 2010 Due on Tuesday, October 12th, 2010 Section 2.1: 6, 12, 14, 16, and 20. Section 2.2: 1, 2, 3, 4, 11.a, 11.b, 11.c, and 23. Additional problem:Consider the iteration in Newton’s method:pn+1=g(pn)whereg(x) =xf(x)f(x)Prove that iff(x) = 0, andf(x)negationslash= 0, theng(x) = 0. Deduce from thisthat the convergence of Newton’s method is quadratic, i.e., if we denote by