L'H?pital's law is a method to determine the undetermined value by deducing the numerator and denominator respectively, and then finding the limit under certain conditions. As we all know, the limit of the ratio of two infinitesimals or the limit of the ratio of two infinitesimals may or may not exist. Therefore, when calculating this kind of limit, it is often necessary to transform it into a limit algorithm or an important limit form for calculation.
Lobida rule is a general method applied to this kind of limit calculation. 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; Second, whether the numerator and denominator are differentiable in a limited area. If these two conditions are satisfied, then take derivative and judge whether the limit after derivative exists.
If it exists, get the answer directly; If it doesn't exist, it means that this undetermined formula can't be solved by L'H?pital's law. If you are not sure, that is, the result is still uncertain, then continue to use L'H?pital's law on the basis of verification. Finding the limit is one of the important contents and the basic part of higher mathematics. L'H?pital's law is used to find the fractional limit of numerator and denominator approaching zero.
Introduction to L'H?pital:
L'H?pital is a French mathematician and a great disseminator of mathematical thoughts. L'H?pital was born in a French aristocratic family in 166 1. Died in Paris on February 2, 704.
He was attacked as a marquis and served as a cavalry officer in the army. Later, he quit the army because of poor eyesight and turned to academic research. He showed his talent for mathematics at an early age. 15 years old, solved Pascal's cycloid problem, and later solved John Middot and Burleigh's challenge to Europe and the steepest descent curve problem.
Later, he gave up his position as an artillery, devoted more time to mathematics, studied calculus under Bernoulli, a Swiss mathematician, and became a major member of the French new analytical school.
L'H?pital's infinitesimal analysis (1696) is the earliest textbook of calculus, and it is also a model work of18th century, in which an algorithm (L'H?pital's law) is created to find the limit of the quotient of two functions that meet certain conditions. In the preface, L'H?pital thanked Leibniz and Bernoulli, especially Johann Middot Bernoulli.