Let p.n/ be a polynomial of degree d in n. Prove that 1. Develop an expression (using the floor or ceiling notation) for the ordinary meaning of rounding off a real number x to the nearest integer. Be...

Let p.n/ be a polynomial of degree d in n. Prove that

1. Develop an expression (using the floor or ceiling notation) for the ordinary meaning of rounding off a real number x to the nearest integer. Be sure your formula properly handles rounding 3:49 to 3, but 3:5 to 4.

2. Develop an expression (using the floor or ceiling notation) for the ones digit of a positive integer. That is, if n D 326, then your expression should evaluate to 6.