https://dananne.org/dw/ 2026-05-06T04:46:12+00:00 https://dananne.org/dw/ https://dananne.org/dw/lib/tpl/codowik/images/favicon.ico text/html 2012-06-25T12:39:09+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=cfsv:cfsv&rev=1340653149&do=diff The Calculus of Functions of Several Variables Answers for selected problems Chapter 1 Chapter 2 Chapter 3 Chapter 4 text/html 2013-07-09T16:00:13+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=cfsv:chapter-1&rev=1373410813&do=diff The Calculus of Functions of Several Variables Answers for selected problems Chapter 1 ---------- Section 1.1 2. (a) $ (4, 5, 0) $ (b) $ (12, 5, 4) $ (c) $ (-12, 8, -{8}) $ (d) $ (-11, 7, -5) $ 5. (a) $ \sqrt{14} $ (b) $ \sqrt{118} $ (c) $ 5\sqrt{14} $ (d) $ 3\sqrt{6} $ 6. (a) $ \sqrt{17} $ (b) $ \sqrt{22} $ (c) $ 2\sqrt{3} $ (d) $ \sqrt{66} $ (e) $ \sqrt{19} $ 11. No 12. (a) $ ||\mathbf{x}|| = \sqrt{5} $, Direction: $ \displaystyle{||\mathbf{u}|| = \frac{1}{\sqrt{5}}(2, 1)}$… text/html 2012-06-25T12:42:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=cfsv:chapter-2&rev=1340653368&do=diff The Calculus of Functions of Several Variables Answers for selected problems Chapter 2 ---------- Section 2.1 4. The curve parametrized by $ f $ is the graph of $ g $. 5. (a) $ \displaystyle{\lim_{n \to \infty}\mathbf{x}_n = \left(\frac{1}{2}, 3\right)}$ (b) $ \displaystyle{\lim_{n \to \infty}\mathbf{x}_n = \left(\sin(1), \cos(1), 1\right)}$ (c) $ \displaystyle{\lim_{n \to \infty}\mathbf{x}_n = \left(0, 3, 4, 0\right)}$ 6. (a) $ \displaystyle{\lim_{t \to \pi}f(t) = \left(0, -1, 3\pi^2\r… text/html 2012-06-25T12:43:56+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=cfsv:chapter-3&rev=1340653436&do=diff The Calculus of Functions of Several Variables Answers for selected problems Chapter 3 ---------- Section 3.1 3. (a) $ \displaystyle{\lim_{(x,y) \to (2,1)}\left(3xy + x^2y + 4\right) = 14}$ (b) $ \displaystyle{\lim_{(x,y,z) \to (1,2,1)}\frac{3xyz}{2xy^2+4z} = \frac{1}{2}}$ (c) $ \displaystyle{\lim_{(x,y) \to (2,0)}\frac{\cos(3xy)}{\sqrt{x^2 + 1}} = \frac{1}{\sqrt{5}}}$ (d) $ \displaystyle{\lim_{(x,y,z) \to (2,1,3)}ye^{2x-3y+z} = e^4}$ 4. (a) $ \displaystyle{\lim_{(x,y) \to (0,0)}\frac{x… text/html 2012-06-25T12:44:48+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=cfsv:chapter-4&rev=1340653488&do=diff The Calculus of Functions of Several Variables Answers for selected problems Chapter 4 ---------- Section 4.1 2. The surface is the graph of $ f $. 3. $ F(s, t) = (s, t, s^2 + t^2) $ 6. $ \{\mathbf{x} \ : \ \mathbf{x} \in \mathbb{R}^n, \mathbf{x} \ne \mathbf{0}\} $ ---------- Section 4.2 1. (a) $ \displaystyle{A(x,y) = \begin{bmatrix}2 & 4\\ 6 & 3\end{bmatrix} \begin{bmatrix}x - 1\\ y - 2\end{bmatrix} + \begin{bmatrix}5\\ 6\end{bmatrix} = \begin{bmatrix}2x + 4y - 5\\ 6x + 3y - 6\end{bm…