http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?action=history&feed=atom&title=L%C3%B6sung_5.2%3A1aLösung 5.2:1a - Versionsgeschichte2026-06-17T16:34:16ZVersionsgeschichte für diese Seite in Online Mathematik Brückenkurs 1MediaWiki 1.11.1http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_5.2:1a&diff=9748&oldid=prevMarkus.bez: Uebersetzung2009-08-10T09:10:12Z<p>Uebersetzung</p>
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<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">When you cancel </del><math>\tan x</math> <del style="color: red; font-weight: bold; text-decoration: none;">on both sides of the equation you might lose those solutions that satisfy </del><math>\tan x=0</math>. <del style="color: red; font-weight: bold; text-decoration: none;">The equation to the right might therefore, potentially, have a reduced set of solutions</del>. <del style="color: red; font-weight: bold; text-decoration: none;">You should consequently use the </del><math>\Leftarrow</math> <del style="color: red; font-weight: bold; text-decoration: none;">arrow</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Durch kürzen von </ins><math>\tan x</math> <ins style="color: red; font-weight: bold; text-decoration: none;">auf beiden Seiten der Gleichung können Lösungen verloren gehen, für die </ins><math>\tan x=0</math> <ins style="color: red; font-weight: bold; text-decoration: none;">gilt</ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Die Gleichung auf der rechten Seite hat deshalb möglicherweise weniger Lösungen</ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Deshalb verwendet man </ins><math>\Leftarrow</math>.</div></td></tr>
<tr><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'> </td><td style="background: #eee; color:black; font-size: smaller;"></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div> </div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins style="color: red; font-weight: bold; text-decoration: none;">Bemerkung: Dabei ist es nicht entscheidend, wenn sich später ergibt, dass beide Gleichungen tatsächlich die selbe Lösungsmenge haben</ins>. <ins style="color: red; font-weight: bold; text-decoration: none;">Was Du zu diesem Zeitpunkt weißt bestimmt, welchen Pfeil Du verwendest</ins>.</div></td></tr>
<tr><td class='diff-marker'>-</td><td style="background: #ffa; color:black; font-size: smaller;"><div><del style="color: red; font-weight: bold; text-decoration: none;">NB</del>. <del style="color: red; font-weight: bold; text-decoration: none;">It doesn't matter that it later turns out that both equations do in fact have the same set of solutions. It is what you know at the time that determines what kind of arrow you use</del>.</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div></div></td></tr>
</table>Markus.bezhttp://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php?title=L%C3%B6sung_5.2:1a&diff=8744&oldid=prevTek: Die Seite wurde neu angelegt: When you cancel <math>\tan x</math> on both sides of the equation you might lose those solutions that satisfy <math>\tan x=0</math>. The equation to the right might the...2009-04-06T07:46:46Z<p>Die Seite wurde neu angelegt: When you cancel <math>\tan x</math> on both sides of the equation you might lose those solutions that satisfy <math>\tan x=0</math>. The equation to the right might the...</p>
<p><b>Neue Seite</b></p><div>When you cancel <math>\tan x</math> on both sides of the equation you might lose those solutions that satisfy <math>\tan x=0</math>. The equation to the right might therefore, potentially, have a reduced set of solutions. You should consequently use the <math>\Leftarrow</math> arrow.<br />
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NB. It doesn't matter that it later turns out that both equations do in fact have the same set of solutions. It is what you know at the time that determines what kind of arrow you use.</div>Tek