d) YesCode:Determine whether x^3 is O(g(x)) for each of these functions g(x). d) g(x) = x^{2} + x^{4} e) g(x) = 3^{x} f) g(x) = x^{3}/2
e) Yes
f) No
Are my answers correct? I took the problem to mean that g(x) < c * x^{3}.
d) YesCode:Determine whether x^3 is O(g(x)) for each of these functions g(x). d) g(x) = x^{2} + x^{4} e) g(x) = 3^{x} f) g(x) = x^{3}/2
e) Yes
f) No
Are my answers correct? I took the problem to mean that g(x) < c * x^{3}.
Hey lamentofking.
I think you have it the other way around. 3^x is an exponential function with infinite numbers of positive powered terms and x^4 has a term higher than x^3. f should be correct (i.e. yes).
Yes.
Could you please re-formulate this clearly? "If x^3 < c * g(x)" eventually, then x^3 = O(g(x)), nothing more to prove. Are you sure you are assuming x^3 < c * g(x)? Next, by c * g(x) do you mean (1/4)x^3 since c = 1/2 and g(x) = (1/2)x^3? That's possible, but why not consider c = 1? Your quote above is not very clear.