![frac{sqrt[3]{n^2-1}+7n^3}{sqrt[4]{n^12+n+1}-n}](https://tex.z-dn.net/?f=frac%7Bsqrt%5B3%5D%7Bn%5E2-1%7D%2B7n%5E3%7D%7Bsqrt%5B4%5D%7Bn%5E12%2Bn%2B1%7D-n%7D "frac{sqrt[3]{n^2-1}+7n^3}{sqrt[4]{n^12+n+1}-n}")
Помогите пожалуйста!!!
Если это облегчит задачу - ответ 7
Ответы на вопрос
Ответил spasibo3pajbrh
0
разделим числитель и знаменатель дроби на n³
![lim_{n to infty} frac{sqrt[3]{n^2-1}+7n^3}{sqrt[4]{n^{12}+n+1}-n} = \ = lim_{n to infty} frac{ sqrt[3]{ frac{1}{n} - frac{1}{ {n}^{2} } } + 7}{ sqrt[4]{1 + frac{1}{ {n}^{11} } + frac{1}{ {n}^{12} }} + frac{1}{ {n}^{4} }} = \ = frac{ sqrt[3]{0 - 0} + 7}{ sqrt[4]{1 + 0+0} + 0} = 7](https://tex.z-dn.net/?f=lim_%7Bn+to+infty%7D+frac%7Bsqrt%5B3%5D%7Bn%5E2-1%7D%2B7n%5E3%7D%7Bsqrt%5B4%5D%7Bn%5E%7B12%7D%2Bn%2B1%7D-n%7D+%3D+%5C+%3D+lim_%7Bn+to+infty%7D+frac%7B+sqrt%5B3%5D%7B+frac%7B1%7D%7Bn%7D+-+frac%7B1%7D%7B+%7Bn%7D%5E%7B2%7D+%7D+%7D+%2B+7%7D%7B+sqrt%5B4%5D%7B1+%2B+frac%7B1%7D%7B+%7Bn%7D%5E%7B11%7D+%7D+%2B+frac%7B1%7D%7B+%7Bn%7D%5E%7B12%7D+%7D%7D+%2B+frac%7B1%7D%7B+%7Bn%7D%5E%7B4%7D+%7D%7D+%3D+%5C+%3D+frac%7B+sqrt%5B3%5D%7B0+-+0%7D+%2B+7%7D%7B+sqrt%5B4%5D%7B1+%2B+0%2B0%7D+%2B+0%7D+%3D+7 "lim_{n to infty} frac{sqrt[3]{n^2-1}+7n^3}{sqrt[4]{n^{12}+n+1}-n} = \ = lim_{n to infty} frac{ sqrt[3]{ frac{1}{n} - frac{1}{ {n}^{2} } } + 7}{ sqrt[4]{1 + frac{1}{ {n}^{11} } + frac{1}{ {n}^{12} }} + frac{1}{ {n}^{4} }} = \ = frac{ sqrt[3]{0 - 0} + 7}{ sqrt[4]{1 + 0+0} + 0} = 7")
Новые вопросы