Questions in category: 多元函数 (Multivariate functions)
分析 >> 数学分析 >> 多元函数
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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)  $(1.007)^{2.98}$

 

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.  $\lim\limits_{(x,y)\rightarrow(0,0)}\frac{xy}{\sqrt{4+3xy}-2}$

 

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