Be f, h, g1, g2 : N → N (monotonously growing) runtimefunctions. Prove the following statements using the definitions ofo-notations:
a) f = o(g) ⇒ f = O(g)
b) f = o(g1) and h = o(g2) ⇒ f + h = o(g1 + g2)
c) f = O(g1) and h = o(g2) ⇒ f – h = o(g1 – g2)
d) f = ⇒(g) ⇒ g = O((f)^2) ((f)^2 is here the function value from fto square)
Be now f, g : R + → R + steady and differentiable. Proveit:
e) If f’ = O(g’), then also f = O(g)
Note: The following applies: ∀n ≥
OR
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