Problem $2.$ Consider the following functions as runtime of different algorithms. Using Limit Comparison

test or other theorems learnt in class, order the functions from fastest to slowest running time:

Functions: $,n!,5^n,n^n,\sqrt[\phantom{2}]{n^{5n+1}}.$

Answer.

Problem $3.$ Consider the following functions as runtime of different algorithms. Using Limit Comparison

test or other theorems learnt in class, order the functions from fastest to slowest running time:

Functions: $,lo{g}_{3}n,(lo{g}_{4}n{)}^{\frac{14}{3}},lo{g}_4(n^{\frac{14}{3}}),n^{\frac{1}{1000}}$

Answer.