Chapter 9  Sequences, L'Hospital's Rule, and Improper Integrals"In the late 17th century, John Bernoulli discovered a rule for calculating limits of fractions whose numerators and denominators both approach zero. The rule is known today as l'Hospital's Rule, after Guillaume Francois Anteoine de l'Hospital (16611704), Marquiz de St. Mesme, a French nobleman who wrote the first differential calculus text, where the rule first appeared in print. We will also use l'Hospital's Rule to compare the rates at which functions of x grow as x becomes large.
In Chapter 6 we saw how to evaluate definite integrals of continuous functions and bounded functions with a finite number of discontinuities on finite closed intervals. These ideas are extended to integrals where one or both limits of integration are infinite, and to integrals whose integrands become unbounded on the interval of integration. Sequences are introduced in preparation for the study of infinite series in Chapter 10." (Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 9." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 443. Print. AP Edition.) 
Chapter 9 reallife math connection.

Lesson 9.2  L'Hospital's Rule
This lesson will teach students how to find the limits of indeterminate forms using L'Hospital's Rule. 