Give the tilde (~) approximations for the following expressions:

1. a. N + 1
2. b. 1 + 1 / N
3. c. (1 + 1 / N)(1 + 2 / N)
4. d. 2N³ - 15N² + N
5. e. lg(2N) / lg(N)
6. f. lg(N² + 1) / lg(N)