Question $2$ : $2$ points

We need a system to compare algorithms and determine which is faster.

Most importantly, we care about how algorithms scale. If we double the size of the input, will the

runtime double or quadruple. If we need to chose between two algorithms, the one that doubles will

perform better then the one that quadruples.

To talk about how algorithms scale with large inputs, we need to use limits$.$ Some important rules of

limits are given below. The limit determines what value the function approaches as the size of the input

increases towards $\backslash$infty $.$