Ответы
Ответ дал:
0
Пример на второй замечательный предел.
![lim_{x to inft{-4}} (9+2x)^{ frac{x+1}{4x+x^2} } = lim_{x to inft{-4}} (1+(8+2x))^{ frac{x+1}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x}*(8+2x) } ]^{ frac{x+1}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x} } ]^{ frac{2(4+x)(x+1)}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x} } ]^{ frac{2(x+1)}{x} } = lim_{x to inft{-4}} (9+2x)^{ frac{x+1}{4x+x^2} } = lim_{x to inft{-4}} (1+(8+2x))^{ frac{x+1}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x}*(8+2x) } ]^{ frac{x+1}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x} } ]^{ frac{2(4+x)(x+1)}{x(4+x)} } = \ \ = lim_{x to inft{-4}} [(1+(8+2x))^{ frac{1}{8+2x} } ]^{ frac{2(x+1)}{x} } =](https://tex.z-dn.net/?f=+lim_%7Bx+to+inft%7B-4%7D%7D+%289%2B2x%29%5E%7B+frac%7Bx%2B1%7D%7B4x%2Bx%5E2%7D+%7D+%3D+lim_%7Bx+to+inft%7B-4%7D%7D+%281%2B%288%2B2x%29%29%5E%7B+frac%7Bx%2B1%7D%7Bx%284%2Bx%29%7D+%7D+%3D+%5C++%5C+%3D+lim_%7Bx+to+inft%7B-4%7D%7D+%5B%281%2B%288%2B2x%29%29%5E%7B+frac%7B1%7D%7B8%2B2x%7D%2A%288%2B2x%29+%7D+%5D%5E%7B+frac%7Bx%2B1%7D%7Bx%284%2Bx%29%7D+%7D+%3D+%5C++%5C+%3D+lim_%7Bx+to+inft%7B-4%7D%7D+%5B%281%2B%288%2B2x%29%29%5E%7B+frac%7B1%7D%7B8%2B2x%7D+%7D+%5D%5E%7B+frac%7B2%284%2Bx%29%28x%2B1%29%7D%7Bx%284%2Bx%29%7D+%7D+%3D+%5C++%5C+%3D+lim_%7Bx+to+inft%7B-4%7D%7D+%5B%281%2B%288%2B2x%29%29%5E%7B+frac%7B1%7D%7B8%2B2x%7D+%7D+%5D%5E%7B+frac%7B2%28x%2B1%29%7D%7Bx%7D+%7D+%3D)
Вас заинтересует
1 год назад
8 лет назад
8 лет назад
8 лет назад