O hk , and g O (hm ) , with m k. Show that f + g O (hm ) .4) Prove that f (h) = 3h5 is in O h5 .5) Prove that f (h) = h2 + 5h17 is in O h2 .

O hk , and g O (hm ) , with m < k. Show that f + g O (hm ) . (1.4) Prove that f (h) = 3h5 is in O h5 . (1.5) Prove that f (h) = h2 + 5h17 is in O h2 . (1.6) Prove that f (h) = h3 is not in O h4 (Hint: Proof by contradiction.) (1.7) Prove that sin(h) is in O (h). (1.8) Find a O h3 approximation to sin h. (1.9) Find a O h4 approximation to ln(1+h). Compare the approximate value to the actual when h = 0.1. How does this approximation compare to the O h3 approximate from Example 1.7 for h = 0.1?