LHopital‘s rule 洛必達法則

sszxzzh發表於2020-10-16

L H o p i t a l ′ s r u l e LHopital's rule LHopital′srule洛必達法則
I n t e r m i n a t e Interminate Interminate  F o r m Form Form 不定型
0 / 0 0/0 0/0 ∞ / ∞ \infty/\infty ∞/∞
lim ⁡ x → a f ( x ) g ( x ) = lim ⁡ x → a f ′ ( x ) g ′ ( x ) \lim_{x\rightarrow a} \frac{f(x)}{g(x)}=\lim_{x\rightarrow a}\frac{f\prime(x)}{g\prime(x)} x→alim​g(x)f(x)​=x→alim​g′(x)f′(x)​
e g 1. eg1. eg1.  lim ⁡ x → ∞ x s i n 1 x \lim_{x\rightarrow \infty}xsin\frac{1}{x} limx→∞​xsinx1​
s o l sol sol translate it into a/b
e g 2. eg2. eg2.  lim ⁡ x → 0 ( 1 s i n x − 1 x ) \lim_{x\rightarrow 0}(\frac{1}{sinx}-\frac{1}{x}) limx→0​(sinx1​−x1​)
s o l sol sol reduction of fractions to a common denominator

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