In this problem you will find O and bounds for functions. In each case you should find and report a value of C and k in the definitions of O and .

(a) Determine the tightest O and bounds that you can for f(n) = 3 50n + 40n + log(25n)

(b) Show that g(n) = (log n) a is O(n) for any nonnegative integer a. Hint: Remember that log n is O(n p ) for all p > 0.

(c) Show that h(n) = 5n 2 + (log n) 3 n log(n 3 ) is (n 2 ) by showing that it is O(n 2 ) and (n 2 ).

2. In this problem you will find O and bounds for functions. In each case you should find and report a value of C and k in the definitions of 0 and 12. 50n+40n + log(25n) (a) Determine the tightest O and bounds that you can for f(n) = (b) Show that g(n) = (log n)" is 0(n) for any nonnegative integer a. Hint: Remember that log n is O(nP) for all p > O (c) Show that h(n) = 5n2 + (log n). n log(n*) is (n*) by showing that it is O(n*) and (n*). (n-) and