Question

1. Order the following functions from slowest growing to fastest growing by inspecting their graphs.

{eq}a. T(n)=n\

b. T(n)=1\

c. T(n)= sqrt{n}\

d. T(n)=n^2\

e. T(n)=log n\

{/eq}

2. Give the big O for the following functions by determining the dominant term.

{eq}a. T(n)=2n^2+3n-7\

b. T(n)=2n^3/n + n^2-3n*n+12quad text{ (Careful. Tricky.)}\

c. T(n)= log{n}+n^{1/2}\

d. T(n)= 2nlog{n}+n^2+100n+1000\

e. T(n)=n^0+27/6\

{/eq}

EXPERT ANSWER

1. Order from slowest to fastest:

{eq} T(n)=n^2\

T(n)=n\

T(n)= sqrt{n}\

T(n)=log n\

T(n)=1\

{/eq}

2. Big-O notation by determining the dominant term:

{eq}a. O(n^2)\

b. O(n^2)\

c. O(n^{1/2})\

d.