For parts (a)-(e), decide if it is true or false. If the statement is true, then prove it (to prove it you will either need to use the definition and find constants or use the limit laws). If the statement is false, then give a reason or a counterexample

a. 10n² = O(n³).

b. n² (n³)

c. 2ⁿ O(2ⁿ⁺¹)

d. n! ((n + 1)!)

e.n = O(n^sin(n))