15. Answer true or false to the following statements. Assume all mentioned functions are symptomatically positive.

16. BONUS QUESTION:

a. Which formula(s) below are equal to F sub (n+2)?

b. It turns out that the ratio of successive Fibonacci numbers have a limit. What is lim n-> infinity (F sub (n+1))/(F sub n)?

15. (8 points) Answer true or false to the following statements. Assume all mentioned func tions are asymptotically positive. a (2 points) If fi(t) = 0(g()) and fx(x) = 0((1)), then fi(1) fa(t) = 0(g()). b. (2 points) If / () =0(91(x)) and 2(x) =0(92(x)), then f(x)/(x) = 92691(E)g(x)). b. c. (2 points) If f(3) = (g(x)) and g(I) =0(()), then f(1) =((:)). d. (2 points) If S(x) = (g(x)), then (x) = $2(g(x)). d. Bomus. (10 points, required for graduate students) This question is extra credit for undergraduates, and mandatory for graduate students. You will get points only if you answer both parts correctly. Consider the Fibonacci numbers defined by Fo = 0, F1 = 1, and the recurrence: F:+1= F+F-1 a. (5 points) Which formula(s) below are equal to Fn+z? A. FR+1+E B. F:+1 C. F.F.-2 D. F. F.-1+1 b. (5 points) It turns out that the ratio of successive Fibonacci mumbers have a limit. What is lim hex F1/F.? A. Va B. C. D. Ve