Consider the Newton’s method iteration in Example 2.
(a) Use initial vector x0 = (1.4, 10) and calculate the successive approximations x1, x2, x3, etc. To what solution of the system of equations (8) do the approximations converge?
(b) Repeat part (a) with x0 = (1.3, 10).
(c) In Example 2 we saw that (4, 5) was a solution of the given system of equations. Is (1.3, 10) closer to (4, 5) or to the limiting point of the sequence you calculated in part (b)?
(d) Comment on your observations in part (c). What do these observations suggest about how easily you can use the initial vector x0 to predict the value of limk→∞ xk (assuming that the limit exists)?
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