l'Hospital's rule
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Topic Notes
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".
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)
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