verify computational rules involving the asymptotic big-O notation. a) Show that (1+0(x))(1+0(x)) = 1+0(x) for x0....

 

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verify computational rules involving the asymptotic big-O notation. a) Show that (1+0(x))(1+0(x)) = 1+0(x) for x0. The precise meaning of this statement is that if f is a function satisfying f(x) = (1 + O(x))(1+0(x)) as r0, then f also satisfies f(x) = 1 + 0(r) as x 0. b) Verify that (1+0(x)) = 1 + 0(x) for x 0. Hint: The formula for the geometric series, or for r < 1, can be helpful. k=0 = verify computational rules involving the asymptotic big-O notation. a) Show that (1+0(x))(1+0(x)) = 1+0(x) for x0. The precise meaning of this statement is that if f is a function satisfying f(x) = (1 + O(x))(1+0(x)) as r0, then f also satisfies f(x) = 1 + 0(r) as x 0. b) Verify that (1+0(x)) = 1 + 0(x) for x 0. Hint: The formula for the geometric series, or for r < 1, can be helpful. k=0 =