Rank the functions by order of growth

Reference no: EM13774567

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

(a) 2^{⌊lg 340⌋}

(b ⌈-26.8⌉

(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)

(d) 23(n!) = O(nⁿ)

Reference no: EM13774567

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