4.7 L'Hospital's Rule

​Introduction

Bubble sort and quicksort are two algorithms that are commonly used in computer programs to sort data sets. For example, these algorithms can be used to sort a list of students in ascending order of age. Take a look at how these algorithms work.
A data set contains a number of elements. When sorting a data set, an algorithm makes comparisons between the elements of the data set and swaps their positions. Hence, the average time required by the algorithm to sort a data set is determined by computing the number of comparison operations.

The average time taken by the bubble sort and quicksort algorithms to sort a data set with n elements is proportional to the number of comparison operations n² and n ln n respectively.

​Formally, an indeterminate form is when you evaluate a limit function, and you get one of the following values:

​​The various types of indeterminate forms include quotients, products, differences, and powers.

​However, you can also apply it to other indeterminate forms by converting them to one of these two forms.

​L'Hôpital's rule is NOT the Quotient Rule