Solved: a. Suppose that 0 < q < p and that F(h) = L + O (hp). Show that F(h) = L + O (hq
Chapter 1, Problem 1.3.15(choose chapter or problem)
a. Suppose that 0 < q < p and that F(h) = L + O (hp). Show that F(h) = L + O (hq ). b. Make a table listing h, h2, h3, and h4 for h = 0.5, 0.1, 0.01, and 0.001, and discuss the varying rates of convergence of these powers of h as h approaches zero. Let c1 and c2 be nonzero constants, and define F(x) = c1F1(x) + c2F2(x) and G(x) = F1(c1 x) + F2(c2x). Show that if = minimum {, }, then as x approaches zero, a. F(x) = c1L1 + c2L2 + O(x ) b. G(x) = L1 + L2 + O(x ).
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