https://dananne.org/dw/ 2026-05-06T06:12:55+00:00 https://dananne.org/dw/ https://dananne.org/dw/lib/tpl/codowik/images/favicon.ico text/html 2016-01-10T11:45:09+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-1&rev=1452455109&do=diff Mathematics 250 - Spring 2016 Homework Section 1.2: 1, 4 Section 2.1: 3, 4, 5, 7 Section 2.2: 1, 2, 3, 4(a) text/html 2016-01-12T06:15:10+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-2&rev=1452608110&do=diff Mathematics 250 - Spring 2016 Homework Section 4.0: 1, 2, 3, 4 text/html 2016-01-14T06:26:58+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-3&rev=1452781618&do=diff Mathematics 250 - Spring 2016 Homework Evaluate the following limits: 1. $\lim\limits_{x \to 1}F(x)$, where $F(x) = (x^2 - 4, 3x + 4)$. 2. $\lim\limits_{t \to \pi}G(t)$, where $G(t) = (\cos(2t), \sin(2t), 2t, \cos(t))$. 3. $\lim\limits_{x \uparrow 2}F(x)$, where $F(x) = (x, \sqrt{4 - x^2})$. 4. $\lim\limits_{t \to \infty}F(t)$, where $F(t) = \left(t^2e^{-2t}, \frac{t+1}{t-1}\right)$. 5. Let $F(t) = (\cos(t), \sin(t))$. Explain why $\lim\limits_{t \to \infty}\|F(t)\|$ exists, but $\lim\li… text/html 2016-01-21T06:20:18+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-4&rev=1453386018&do=diff Mathematics 250 - Spring 2016 Homework Section 4.1: 1, 2, 3, 4, 5, 6, 9, 16, 17, 24, 27 Note: For Exercise 27, you don't need to draw the curves (although you may want to draw them using wxMaxima). text/html 2016-01-21T07:09:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-5&rev=1453388942&do=diff Mathematics 250 - Spring 2016 Homework Section 4.2: 2, 3, 5, 25 text/html 2016-01-26T07:30:07+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-6&rev=1453822207&do=diff Mathematics 250 - Spring 2016 Homework Section 4.2: 6, 7, 8, 9, 10, 11, 12, 13, 14, 18 (parts 1 - 3), 24 text/html 2016-01-28T05:59:35+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-7&rev=1453989575&do=diff Mathematics 250 - Spring 2016 Homework Section 4.3: 1, 2, 3, 4, 11, 23, 25 text/html 2016-02-03T06:40:41+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-8&rev=1454510441&do=diff Mathematics 250 - Spring 2016 Homework Section 4.3: 6, 13, 14, 16 Also: * Find the natural parametrization of the curve $C$ parametrized by $F(t) = (t, \cos(2t), \sin(2t))$ for $0 \le t \le \pi$. * Find the natural parametrization of the curve $C$ parametrized by $F(t) = (e^t\cos(t), e^t\sin(t), e^t)$ for $0 \le t \le 2\pi$. * Find the curvature of the curve parametrized by $F(t) = (t, t^2, t^3)$$t = 1$$y = x^2$$x = 1$$y = \sin(x)$$x = \frac{\pi}{2}$$G(\tau) = \left(\frac{\tau}{\sqrt{5… text/html 2016-02-02T09:54:57+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-9&rev=1454435697&do=diff Mathematics 250 - Spring 2016 Homework Section 6.0: 1, 2, 3, 5 text/html 2016-02-11T07:10:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-10&rev=1455203431&do=diff Mathematics 250 - Spring 2016 Homework Section 6.1: 1, 3, 4, 7, 11, 13, 19, 21, 22, 23 Also: * Let $\displaystyle{f(x, y) = \frac{x^2 - y^2}{x^2 + y^2}}$. * Show if $(x, y) = (t, 0)$, then $\displaystyle{\lim_{t \to 0}f(x, y) = 1}$. * Show if $(x, y) = (0, t)$, then $\displaystyle{\lim_{t \to 0}f(x, y) = -1}$. * Show if $(x, y) = (t, t)$, then $\displaystyle{\lim_{t \to 0}f(x, y) = 0}$. * Does $\displaystyle{\lim_{(x, y) \to (0, 0)}f(x, y)}$ exist? Explain. * Let $\displayst… text/html 2016-02-14T09:54:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-11&rev=1455472465&do=diff Mathematics 250 - Spring 2016 Homework Section 6.2: 1, 2, 3, 6 Section 6.3: 1, 2, 9, 10, 14, 18 text/html 2016-02-18T06:20:59+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-13&rev=1455805259&do=diff Mathematics 250 - Spring 2016 Homework Section 6.5: 1, 2, 3 text/html 2016-02-21T10:49:04+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-14&rev=1456080544&do=diff Mathematics 250 - Spring 2016 Homework Section 6.5: 13, 14, 16, 19 text/html 2016-02-23T06:36:25+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-15&rev=1456238185&do=diff Mathematics 250 - Spring 2016 Homework Section 7.1: 1 (except (k) and (l)), 5, 6 Hint for 5 and 6: Look for critical points of $\|(x, y, z)\|^2$, where $(x, y, z)$ is a point on the given surface. Intuitively, why should these functions have minimum values? text/html 2016-02-25T11:51:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-16&rev=1456429896&do=diff Mathematics 250 - Spring 2016 Homework Section 7.2: 1, 2(a), 3, 4, 7 Also: Find the second-order Taylor polynomial for each of the following: * $f(x, y, z) = 4xyz + 6xy^2 + 4x^2z^2$ at $(1, -1, 1)$ * $f(x, y, z) = e^{x + y + z}$ at $(0, 0, 0)$ Answers: * $p(x, y, z) = 6 + 10(x - 1) - 8(y + 1) + 4(z - 1) + 8(x - 1)^2 \\+ 6(y + 1)^2 + 4(z - 1)^2 - 8(x - 1)(y + 1) + 4(y + 1)(z - 1) + 12(x - 1)(z - 1)$ * $p(x, y, z) = 1 + x + y + z + \frac{1}{2}x^2 + \frac{1}{2}y^2 + \frac{1}{2}z^2 + x… text/html 2016-02-28T10:07:26+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-17&rev=1456682846&do=diff Mathematics 250 - Spring 2016 Homework Section 7.3: 1, 10 text/html 2016-03-01T09:32:45+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-18&rev=1456853565&do=diff Mathematics 250 - Spring 2016 Homework Section 7.3: 2(except (i)), 3, 11, 12 text/html 2016-03-03T09:01:04+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-19&rev=1457024464&do=diff Mathematics 250 - Spring 2016 Homework Section 7.4: 1bcel, 2, 3, 4 text/html 2016-03-16T10:34:22+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-20&rev=1458149662&do=diff Mathematics 250 - Spring 2016 Homework Section 7.5: 1, 2, 3, 5, 6, 7, 8 text/html 2016-03-19T06:59:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-21&rev=1458395945&do=diff Mathematics 250 - Spring 2016 Homework Section 9.1: 3 (Estimate each integral with a Riemann sum using four subrectangles, and evaluating the function at the midpoint of each subrectangle.) text/html 2016-03-22T06:10:27+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-22&rev=1458652227&do=diff Mathematics 250 - Spring 2016 Homework Section 9.2: 1, 2 (evaluate, don't estimate), 3, 4, 11, 18 text/html 2016-03-29T05:28:11+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-23&rev=1459254491&do=diff Mathematics 250 - Spring 2016 Homework Section 9.2: 5, 6, 14 text/html 2016-03-31T07:50:40+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-24&rev=1459435840&do=diff Mathematics 250 - Spring 2016 Homework Section 9.4: 1, 2 And: Let $B$ be the region bounded by the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a > 0$ and $b > 0$, and let $D$ be the closed disk $\bar B((0,0); 1)$. Show that $\displaystyle{\int\int_B dA = ab\int\int_D dA}$, and hence that the area of $B$ is $ab\pi$. Hint: Consider the transformation $T(u, v) = (au, bv)$. text/html 2016-04-03T07:10:12+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-25&rev=1459692612&do=diff Mathematics 250 - Spring 2016 Homework Section 9.2: 7, 9, 10 Section 9.4: 7, 10 And: Let $\displaystyle{I = \int_{-\infty}^\infty e^{-\frac{x^2}{2}}dx}$. * Show that $\displaystyle{I^2 = \int_{-\infty}^\infty \int_{-\infty}^\infty e^{-\frac{x^2 + y^2}{2}}dxdy}$. * Use polar coordinates to show that $I^2 = 2\pi$ and, hence, that $I = \sqrt{2\pi}$. text/html 2016-04-05T07:45:47+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-26&rev=1459867547&do=diff Mathematics 250 - Spring 2016 Homework Section 9.4: 9ab, 14, 15, 23, 24, 29, 30 Also: 1. Evaluate $\displaystyle{\int\int\int_B \frac{1}{\sqrt{x^2+y^2+z^2}} \ dV}$, where $B$ is the region in $\mathbb{R}^3$ between the spheres with equations $x^2 + y^2 + z^2 = 4$ and $x^2 + y^2 + z^2 = 9$. 2. Evaluate $\displaystyle{\int\int\int_B \sin\left(\sqrt{x^2+y^2+z^2}\right) \ dV}$, where $B$ is the region in $\mathbb{R}^3$ described by $x \ge 0$, $y \ge 0$, $z \ge 0$, and $x^2 + y^2 + z^2 \le 1$. … text/html 2016-04-13T08:18:31+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-28&rev=1460560711&do=diff Mathematics 250 - Spring 2016 Homework Section 10.1: 1, 2, 3, 4, 7, 8, 9, 12, 13, 14, 20a (Correction: $e^{\frac{1}{16}}$ should be $e^{\frac{1}{2}}$) text/html 2016-04-17T10:07:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-29&rev=1460912820&do=diff Mathematics 250 - Spring 2016 Homework Section 10.2: 1(d) text/html 2016-04-21T08:32:05+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=math-250:m250-f16-hw:hw-30&rev=1461252725&do=diff Mathematics 250 - Spring 2016 Homework Section 10.2: 1abcefgh, 4, 7 And: 1. Use Green's theorem to show that the area of a circle of radius $r$ is $\pi r^2$. 2. Use Green's theorem to find the area of the region $B$ enclosed by the hypocycloid $x^{\frac{2}{3}} + y^{\frac{2}{3}} = a^{\frac{2}{3}}$, where $a > 0$. Note: $\partial B$$\alpha(t) = (a\cos^3(t), a\sin^3(t))$$0 \le t \le 2\pi$$\frac{3}{8}\pi a^2$