https://dananne.org/dw/ 2026-05-06T04:46:13+00:00 https://dananne.org/dw/ https://dananne.org/dw/lib/tpl/codowik/images/favicon.ico text/html 2012-06-25T11:10:00+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-1&rev=1340647800&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 1 ---------- Section 1.1 4. (a) $ y = 4(x - 1) + 2 $ (b) $ y = 2(x - 1) + 2 $ (c) $ y = 3(x - 1) + 1 $ (d) $ y = 4(x - 2) + 4 $ 5. For $ 6 $ digits, $ n = 5624 $. 6. $ n \ge 201 $ 7. (a) $ p = 101 $ (b) $ |m_n - 2| < 0.01 $ when $ n > p $ 8. (a) $ a_{20} = 0.9996 $ to four decimal places. $ a_{20} = 2.6533 $$ a_{20} = 41.1032 $$ \displaystyle{a_n = \frac{1… text/html 2012-06-25T11:28:46+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-2&rev=1340648926&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 2 ---------- Section 2.1 1. (a) $ y $ is a function of $ x $ Relationship: $ y = 2x $ Domain $ = [0, S] $, where $ S $ is the maximum speed of the train Range $ = [0, 2S] $ (c) $ y $ is a function of $ x $ Domain $ = [0, 8760] $$ = [221.5, 238.9] $$ y $$ x $$ y $$ x $$ y = 2\sqrt{\pi x} $$ = (0, \infty) $$ = (0, \infty) $$ y $$ x $$ \displaystyle{y = \begin{cases}41,& \text{if } 0 < x \le 1,\\ 58… text/html 2012-06-25T11:25:32+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-3&rev=1340648732&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 3 ---------- Section 3.1 1. (b) $ m = 1 $ 2. (a) $ o(h) $ (b) $ O(h) $ (c) $ o(h) $ (d) $ o(h) $ (e) $ o(h) $ (f) Neither 3. (b) $ R_T $ is $ O(h) $, but not $ o(h) $. (c) $ R_S $ is both $ o(h) $ and $ O(h) $. (d) $ S $ is the best affine approximation to $ f $$ 9 $$ \sqrt{10} \approx S(10) = \displaystyle{\frac{19}{6}} = 3.167 $$ \sqrt{10} $$ 3.162 $$ T(x) = 4(x - 1) + 2 $$ f'(1) = 4 $$ T(x) =… text/html 2012-06-25T11:30:38+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-4&rev=1340649038&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 4 ---------- Section 4.1 1. (a) The area is between $ \dfrac{77}{60} $ and $ \dfrac{25}{12} $. (b) The area is between $ 14 $ and $ 30 $. (c) The area is between $ 6 $ and $ 14 $. (d) The area is between $ \dfrac{\sqrt{2}\pi}{4} $ and $ \dfrac{(2 + \sqrt{2})\pi}{4} $. $ \displaystyle{\frac{81}{4} \le \int_1^4 3xdx \le \frac{99}{4}}$$ \displaystyle{-\frac{2\pi}{3} \le \int_{-\pi}^\pi \cos(x)dx \le \f… text/html 2012-06-25T11:32:15+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-5&rev=1340649135&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 5 ---------- Section 5.1 1. $ \displaystyle{\lim_{h \to 0}\frac{\tan^2(h)}{h} = 0}$ 3. $ \displaystyle{\lim_{h \to 0}\frac{h^2\sin(h)}{h^2} = 0}$ and $ \displaystyle{\lim_{h \to 0}\frac{h^2\sin(h)}{h^3} = 1}$ 5. $ \displaystyle{\lim_{h \to 0}\frac{\sin^2(3h)}{h^2} = 9}$ 7. (a) $ \displaystyle{P_4(x) = 2x - \frac{4x^3}{3}}$ (c) $ \displaystyle{P_4(z) = 2 + \frac{1}{4}(z - 4) - \frac{1}{64}(z - 4)^2 + \fr… text/html 2012-06-25T11:33:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-6&rev=1340649234&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 6 ---------- Section 6.1 1. (a) $ f'(x) = 6e^{2x} $ (c) $ h'(z) = 3z(15z^3 - 30z + 2)e^{5z^3} $ (e) $ \displaystyle{g'(z) = \frac{3}{2}(1 - x)e^{-x}}$ (g) $ \displaystyle{f'(s) = \frac{(1 + 6s)e^{-2s} + 6}{(e^{-2s} + 2)^2}}$ 2. (a) $ \displaystyle{\int 3e^{2x}dx = \frac{3}{2}e^{2x} + c}$ (c) $ \displaystyle{\int 4te^{3t}dt = \frac{4}{3}te^{3t} - \frac{4}{9}e^{3t} + c}$ (e) $ \displaystyle{\int z^2 e^z… text/html 2012-06-25T11:35:06+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-7&rev=1340649306&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 7 ---------- Section 7.1 1. (a) $ w + z = 1 + 3i $ (c) $ 3w - 2z = 13 - 26i $ (e) $ zw = 22 + 29i $ (f) $ \displaystyle{\frac{z}{w} = -\frac{34}{25} + \frac{13}{25}i}$ (g) $ |z| = \sqrt{53} $ (i) $ \Re(z - w) = -5 $ (j) $ \Im(3z + w) = 17 $ 2. (a) $ \displaystyle{\Re\left(\frac{1}{i}\right) = 0}$, $ \displaystyle{\Im\left(\frac{1}{i}\right) = -1}$ (c) $ \displaystyle{\Re\left(\frac{3-4i}{-2+3i}\righ… text/html 2012-06-25T11:41:28+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:chapter-8&rev=1340649688&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 8 ---------- Section 8.1 1. (a) $ \displaystyle{x(t) = \frac{1}{3}t^3 - 2t + 3}$ (c) $ \displaystyle{y(t) = \frac{2}{3}t^{\frac{3}{2}} - \frac{11}{3}}$ 3. (a) $ \displaystyle{x(t) = -16t^2 + 20t + 100}$ (b) $ \displaystyle{t = \frac{5}{8}}$ seconds (c) $ 106.25 $ feet (d) $ \displaystyle{t = \frac{5}{8}(1 + \sqrt{17}) = 3.2019}$ seconds, rounded to 4 decimal places 4. (a) [Section 8.1 - Problem 4. (… text/html 2012-06-25T11:08:36+00:00 Anonymous (anonymous@undisclosed.example.com) https://dananne.org/dw/doku.php?id=de2de:de2de&rev=1340647716&do=diff Differential Equations to Difference Equations Answers for selected problems Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8