11. 计算下列数的近似值.
Posted by haifeng on 2023-03-25 08:29:46 last update 2023-03-25 08:29:46 | Answers (1) | 收藏
计算下列数的近似值.
(1) $(1.007)^{2.98}$
Questions in category: 多元函数 (Multivariate functions)
分析 >> 数学分析 >> 多元函数
12. 求下列函数的全微分
Posted by haifeng on 2023-03-25 08:16:36 last update 2023-03-25 08:55:53 | Answers (1) | 收藏
(4) $z=\frac{2x-y}{x+2y}$
(5) $u=x(x+y^2+z^3)$
13. 设 $r=\sqrt{x^2+y^2+z^2}$, 证明: $\frac{\partial^2(\ln r)}{\partial x^2}+\frac{\partial^2(\ln r)}{\partial y^2}+\frac{\partial^2(\ln r)}{\partial z^2}=\frac{1}{r^2}$.
Posted by haifeng on 2023-03-25 08:03:12 last update 2023-03-25 08:03:12 | Answers (1) | 收藏
设 $r=\sqrt{x^2+y^2+z^2}$, 证明: $\frac{\partial^2(\ln r)}{\partial x^2}+\frac{\partial^2(\ln r)}{\partial y^2}+\frac{\partial^2(\ln r)}{\partial z^2}=\frac{1}{r^2}$. 即 $\Delta(\ln r)=\frac{1}{r^2}$.
14. 证明下列极限不存在.
Posted by haifeng on 2023-03-17 22:39:05 last update 2023-03-17 22:39:05 | Answers (1) | 收藏
1.
$\lim\limits_{(x,y)\rightarrow(0,0)}\frac{x+y}{x-y}$
15. [多元函数] 求下列函数的极限
Posted by haifeng on 2023-03-17 22:33:20 last update 2023-03-17 22:35:04 | Answers (1) | 收藏
1. $\lim\limits_{(x,y)\rightarrow(0,0)}\frac{xy}{\sqrt{4+3xy}-2}$