- Home
- CLEP Calculus
- Applications of the Derivative
l'Hospital's rule
- Intro Lesson5:50
- Lesson: 1a2:00
- Lesson: 1b2:15
l'Hospital's rule
Remember that one tricky Limits section that required intense algebraic manipulation to avoid getting 0/0 or infinity/infinity limits? We will now revisit it again, but with the knowledge of derivatives. In this section, we will learn how derivatives enable us to efficiently evaluate the limits of a function using the "L'Hospital's rule".
Lessons
Note *l'Hôpital's Rule applies to 2 types of indeterminate forms:
type 00 (that is, limx →c f(x)=0 and limx →cg(x)=0)
or
type ∞∞ (that is, limx →c f(x)=±∞ and limx →cg(x)=±∞)
Then according to l'Hôpital's Rule: limx →c g(x)f(x)= limx →c g′(x)f′(x)
type 00 (that is, limx →c f(x)=0 and limx →cg(x)=0)
or
type ∞∞ (that is, limx →c f(x)=±∞ and limx →cg(x)=±∞)
Then according to l'Hôpital's Rule: limx →c g(x)f(x)= limx →c g′(x)f′(x)
- IntroductionEvaluating the limit of the form:
limx →c g(x)f(x) - 1.Evaluating the limit.
Find:a)limx →1 x−1lnxb)limx →∞ x−1lnx