Rank the following functions by order of growth if two or

Question

1. Evaluate the following. Show all of your work.

(a) 2^{⌊lg 340⌋}

(b ⌈-26.8⌉

(c) ⌊lg 1026⌋

(d) 4 + 8 + 12 + ... + 396 + 400

(e) lg (32⁸⁸⁸⁴⁴⁴)

2. Rank the following functions by order of growth. If two or more are of the same order (f(n) and g(n) are in the same class if and only if f(n) = T(g(n))), indicate which.

7n                   2ⁿ                   3n (lg n)                  55ln n

2n⁵ -n³ +n      lg n                  n+ lg n                           2^n-1

n³ + lg n            n³                   2 ⁿ⁺²                        20n⁵+1

n ⁴                 lg (lg n)        n ^4-ε    where  0< ε <1       n!

3. Are the following equations true? (Yes or No) Justify your answer.

(a) 3n² - 5n = T(n²)

(b) n² + 7n = O(n)

(c) 3ⁿ = O(n!)

(d) 23(n!) = O(nⁿ)