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File:Hopital sin x by -0.5x.png

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for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with
1789: 471:{\displaystyle \left\{{\begin{array}{ll}{\frac {f(x)}{g(x)}}&{\mbox{ if }}x\neq 0\\{\frac {f'(x)}{g'(x)}}&{\mbox{ if }}x=0\\\end{array}}\right.} 1357: 1507:"}},"text\/plain":{"en":{"P275":"Creative Commons Attribution-ShareAlike 2.0 Generic"}}}}": --> 1711: 1190:; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled 56: 52: 48: 42: 101: 1615: 1598: 1581: 1564: 1547: 1530: 1466: 69: 1296: 1450: 1739: 1377: 1363: 1182: 1749: 1514: 1425: 1258: 1254: 1250: 1246: 1242: 1187: 131: 1295:– If you remix, transform, or build upon the material, you must distribute your contributions under the 1701: 1443:"}},"text\/plain":{"en":{"P6216":"copyrighted"}}}}": --> 1351: 1706: 109: 478:
completes the function definition such that a continuous function results, by l'Hôpital's rule.
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Continuous completion of f(x)/g(x) by l'Hopital's rule
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84: 711:"Continuous completion of f(x)/g(x) by l'Hopital's rule" 446: 382: 128:
Continuous completion of an example function quotient
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This has several advantages; see  1409:Example application of l'Hôpital's rule 1697:The following 3 pages use this file: 120: 1328: 1198:http://www.gnu.org/copyleft/fdl.html 170:{\displaystyle {\frac {f(x)}{g(x)}}} 1628: 1230: 1225: 13: 1414: 1408: 1339: 1323: 1216: 1165: 297:, the quotient is undefined since 121: 67: 1803: 1413: 1399: 1332: 1283:Under the following conditions: 1237:This file is licensed under the 1229: 1224: 1218: 1174: 1173: 88: 31: 21: 1396: 1717: 1632: 1395: 1204:GNU Free Documentation License 1193:GNU Free Documentation License 1183:GNU Free Documentation License 437: 431: 418: 412: 373: 367: 359: 353: 313: 307: 243: 237: 214: 208: 193: 187: 161: 155: 147: 141: 26: 1: 1692: 1421:Items portrayed in this file 1159: 7: 1736:Usage on ckb.wikipedia.org 332:. Defining the function as 220:{\displaystyle f(x)=sin(x)} 10: 1808: 1786:Usage on th.wikipedia.org 1776:Usage on su.wikipedia.org 1766:Usage on pl.wikipedia.org 1756:Usage on id.wikipedia.org 1746:Usage on fa.wikipedia.org 1726:Usage on bn.wikipedia.org 1702:L'Hôpital's rule 1344:image could be re-created 1297:same or compatible license 261:{\displaystyle g(x)=-0.5x} 123: 1629: 1358:Commons:Media for cleanup 16: 1398: 1378:Vector version available 1364:vector version available 1263: 1241:Attribution-Share Alike 1188:Free Software Foundation 1089:"defined as f'(0)/g'(0)" 930:"f(x)/g(x) " 492: 95:This is a file from the 36: 1707:User:Spiderdrew/sandbox 1686: 99:. Information from its 472: 326: 325:{\displaystyle g(0)=0} 291: 262: 221: 171: 102:description page there 41:Size of this preview: 1780:Aturan L'Hôpital 1770:Reguła de l’Hospitala 1760:Aturan L'Hôpital 1665:13:44, 19 August 2016 473: 327: 292: 263: 222: 172: 1384:) does not need the 990:"g'(x) " 963:"f'(x) " 336: 301: 275: 231: 181: 132: 1278:– to adapt the work 486:Gnuplot source code 290:{\displaystyle x=0} 47:Other resolutions: 468: 463: 450: 386: 322: 287: 258: 217: 167: 61:1,666 × 966 pixels 57:1,024 × 594 pixels 1718:Global file usage 1690: 1515:copyright license 1481:copyright license 1407: 1393: 1392: 1243:4.0 International 1215: 1214: 1156: 1155: 449: 441: 385: 377: 165: 117: 116: 97:Wikimedia Commons 32:Global file usage 1799: 1682:Jochen Burghardt 1677: 1639: 1451:copyright status 1437:copyright status 1405: 1371: 1336: 1335: 1329: 1319: 1316: 1313: 1310: 1307: 1299:as the original. 1239:Creative Commons 1233: 1232: 1228: 1227: 1222: 1221: 1211: 1208: 1205: 1202: 1199: 1177: 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