Ответ:
Объяснение:
Используем предел
Перепишем исходный предел
Проверяем в Maxima
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Answers & Comments
Ответ:
Объяснение:
Используем предел![\lim_{n \to \infty} (1+\frac{1}{n})^n=e \lim_{n \to \infty} (1+\frac{1}{n})^n=e](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%281%2B%5Cfrac%7B1%7D%7Bn%7D%29%5En%3De)
Перепишем исходный предел![\lim_{n \to \infty} (1+\frac{1}{9n^{2}+4n+2})^{3n^{2}+5n+4}= \lim_{n \to \infty} (1+\frac{1}{9n^{2}})^{3n^{2}}=\lim_{n \to \infty} ((1+\frac{1}{9n^{2}})^{9n^{2}})^{\frac{1}{3} }=e^{\frac{1}{3}} \lim_{n \to \infty} (1+\frac{1}{9n^{2}+4n+2})^{3n^{2}+5n+4}= \lim_{n \to \infty} (1+\frac{1}{9n^{2}})^{3n^{2}}=\lim_{n \to \infty} ((1+\frac{1}{9n^{2}})^{9n^{2}})^{\frac{1}{3} }=e^{\frac{1}{3}}](https://tex.z-dn.net/?f=%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%281%2B%5Cfrac%7B1%7D%7B9n%5E%7B2%7D%2B4n%2B2%7D%29%5E%7B3n%5E%7B2%7D%2B5n%2B4%7D%3D%20%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%281%2B%5Cfrac%7B1%7D%7B9n%5E%7B2%7D%7D%29%5E%7B3n%5E%7B2%7D%7D%3D%5Clim_%7Bn%20%5Cto%20%5Cinfty%7D%20%28%281%2B%5Cfrac%7B1%7D%7B9n%5E%7B2%7D%7D%29%5E%7B9n%5E%7B2%7D%7D%29%5E%7B%5Cfrac%7B1%7D%7B3%7D%20%7D%3De%5E%7B%5Cfrac%7B1%7D%7B3%7D%7D)
Проверяем в Maxima