L'H?pital's Law (Theorem)
Let the functions f(x) and F(x) satisfy the following conditions:
1，x→a，lim f(x)=0，lim F(x)=0。
2. Both F(x) and F(x) can be derived in an eccentric neighborhood of point A, and the derivative of f (x) is not equal to 0;
3. When x→a, lim (f ′ (x)/f ′ (x)) exists or is infinite.
Then when x→a, lim(f(x)/F(x))=lim(f'(x)/F'(x)).
Extended data:
Before applying L'H?pital's law, two tasks must be completed: first, whether the limits of numerator and denominator are all equal to zero (or infinity); The second is whether the numerator and denominator are differentiable in a limited area.
If these two conditions are met, then take derivative and judge whether the limit after derivative exists: if it exists, get the answer directly; If it does not exist, it means that this infinitive cannot be solved by L'H?pital's law. If it is uncertain, that is, the result is still undecided, then continue to use the Lobida rule on the basis of verification.
Named after L'H?pital.
L'H?pital was born into a noble family. He has been interested in mathematics since he was a child and has a certain talent. He worked out a Pascal problem in his teens, but when he grew up, he did not engage in his favorite math career, but obeyed military service and was discharged from the army because of his poor eyesight.
Since then, on the one hand, he inherited his ancestral business, on the other hand, he began to delve into the mathematical problems he always liked, and at the same time (1964) he was very interested in the calculus just discovered by Newton Leibniz, but he couldn't understand it (at that time, there were no more than five people in the world who knew calculus, including Leibniz, Newton, John Bernoulli, Jacob Bernoulli and Huygens).
Baidu Encyclopedia-Lobida Rule