Solve & Explain all problems please

1. [10 pts) Explain the meaning of the following expression a. f(n) = O(1) b. f(n) = O(n) 2. [60 pts] Use the definition of Big O to prove: f(n)=n logn th*n* +100n=O(n^) b. 2n+3 = 0(2") c. In(n) = O(logn) d. k.=0(n) a. =1 1.6 e. 12 + n log n=0(n.1.6) 5n f. On') Inn 3. (30 pts) Let fi = O(g), S. =0(82) prove a. S+= (max(88.)) b. k = 0(g) C./ = O(g).g = O(h), then f = 0(h)