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thethen

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thethen
† thethen, adv. Obs. Forms: 2–3 (Orm.) þeþenn, 3 ðeðen, 4 þi-, þei-, þeyþen, þeiþin, thythen, þeden, -in, 4–5 þeþen, -þin, -thyn, theþen, -then, -thyn, 5 þ-, thethin, -thyne. [Early ME., a. ON. þeðan, Icel. þaðan (MSw. thædhan, obs. Da. deden), f. root of the with suffix of ‘motion from’, as in heth... Oxford English Dictionary
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whethen
† ˈwhethen, adv. Obs. Forms: 3 weðen, queðen, 4 wheþin, -yn, whethene, queþen, quiþen, queiþin, queyþen, weþen, wethen, wythenne, 4–5 wheþen(e, whethen, quethen, 5 wheþon, whethyn, whythene, -yne, quethin, qu-, qwethun. [a. ON. hvaðan (MSw. hwädhan, MDa. hvæden; f. root of who + ðan as in heðan, þeð... Oxford English Dictionary
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thyne
† thyne, adv. Sc. and north. dial. Obs. (ðaɪn) Forms: 4 þien, þein, þine, 4–6 thine, 4–7 thyne, 5 þeine, þeyn, 5–6 thyn, 6 thin. [App. reduced from thethen; cf. hyne, syne, whyne.] = thence. (Also prec. by fra, from.)c 1330 R. Brunne Chron. (1810) 190 Þe templers ilk a dele failed & þien fled. 13.. ... Oxford English Dictionary
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syne
▪ I. syne, adv. (conj.) Sc. and north. dial. (saɪn) Forms: 4 seine, syn, 4–6 (9) sine, 5 seyn(e, syen(e, syon, (8–9 saan), 4– syne. [Contracted form of ME. sethen, sithen, perh. influenced by ON. s{iacu}ðan; cf. hyne, thyne, whyne for hethen, thethen, whethen. The northern-English spellings with -ei... Oxford English Dictionary
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Estimate the value of $y_1(3)-y_2(3)$ with $y'=\arctan(y+x+\cos(y)^2)$ and $y_1(0)=1, y_2(0)=2$ Show that $y_1$ and $y_2$ exist, determin the sign and estimate the value of $y_1(3)-y_2(3)$ with $y'=\arctan(y+x+\cos(y)...
TheThen $$\begin{align} |y_1(x)-y_2(x)|&=\Bigl|y_1(0)-y_2(0)+\\\ &\quad \int_0^x(\arctan(y_1(t)+t+\cos^2y_1(t))-\arctan(y_2(t)+t+\cos^2y_2(t)))\,dt\Bigl
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process
▪ I. process, n. (ˈprɒsɛs, ˈprəʊsɛs) Forms: 4–7 proces (also pl.), -cesse, (5 procese, -ceis, -ses, -seys, -sis(se, -ssesse, 5–6 prosses), 5– process. [ME. proces, a. F. procès (13th c. in Godef.), ad. L. prōcess-us (u-stem) advance, progress, process, lapse of time, f. ppl. stem of prōcēd-ĕre to pr... Oxford English Dictionary
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file
▪ I. file, n.1 (faɪl) Forms: 1 fiil, féol, 3 south. vile, (5 vyle), 4–7 fyle, 4– file. [OE. féol (Anglian f{iacu}l) = MDu., MLG. vîle (Du. vijl, LG. file), OHG. fîla, fîgila, fîhala (MHG. vîle, vîgel, mod.Ger. feile); ON. with anomalous initial consonant þél (mod.Icel. þjöl, MSw. fäl, MDa. fel; the ... Oxford English Dictionary
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