https://www.nplg.gov.ge/wikidict/index.php?action=history&feed=atom&title=%E1%83%A2%E1%83%94%E1%83%98%E1%83%9A%E1%83%9D%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%AC%E1%83%99%E1%83%A0%E1%83%98%E1%83%95%E1%83%98 2026-05-04T06:06:44Z ამ გვერდის შესწორებათა ისტორია ვიკიში MediaWiki 1.19.24 https://www.nplg.gov.ge/wikidict/index.php?title=%E1%83%A2%E1%83%94%E1%83%98%E1%83%9A%E1%83%9D%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%AC%E1%83%99%E1%83%A0%E1%83%98%E1%83%95%E1%83%98&diff=219157&oldid=prev 2024-02-14T20:32:38Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←წინა ვერსია</td> <td colspan='2' style="background-color: white; color:black;">20:32, 14 თებერვალი 2024-ის ვერსია</td> </tr><tr><td colspan="2" class="diff-lineno">ხაზი 12:</td> <td colspan="2" class="diff-lineno">ხაზი 12:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:::(1 + x)&lt;sup&gt;m&lt;/sup&gt; = 1+mx+...+m(m-1)(m-2)... (m-n+1) x&lt;sup&gt;n&lt;/sup&gt; /n! + .. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:::(1 + x)&lt;sup&gt;m&lt;/sup&gt; = 1+mx+...+m(m-1)(m-2)... (m-n+1) x&lt;sup&gt;n&lt;/sup&gt; /n! + .. &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:::e&lt;sup&gt;x&lt;/sup&gt; = 1 + x/1! + x&lt;sup&gt;2&lt;/sup&gt;/2! + x&lt;sup&gt;3&lt;/sup&gt;/3! +… +x&lt;sup&gt;n&lt;/sup&gt; /n! + . . .</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>:::e&lt;sup&gt;x&lt;/sup&gt; = 1 + x/1! + x&lt;sup&gt;2&lt;/sup&gt;/2! + x&lt;sup&gt;3&lt;/sup&gt;/3! +… +x&lt;sup&gt;n&lt;/sup&gt; /n! + . . .</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:::sinx = x <del class="diffchange diffchange-inline">= </del>x&lt;sup&gt;3&lt;/sup&gt; / 3! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n+1&lt;/sup&gt;/(2n+1)! + . . .</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:::sinx = x <ins class="diffchange diffchange-inline">- </ins>x&lt;sup&gt;3&lt;/sup&gt; / 3! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n+1&lt;/sup&gt;/(2n+1)! + . . .</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>:::cosx = 1-x&lt;sup&gt;2&lt;/sup&gt;/2! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n&lt;/sup&gt; / (2n)! +&#160; . . .</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div>:::cosx = 1 - x&lt;sup&gt;2&lt;/sup&gt;/2! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n&lt;/sup&gt; / (2n)! +&#160; . . .</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> </table>

Echelidze https://www.nplg.gov.ge/wikidict/index.php?title=%E1%83%A2%E1%83%94%E1%83%98%E1%83%9A%E1%83%9D%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%AC%E1%83%99%E1%83%A0%E1%83%98%E1%83%95%E1%83%98&diff=219156&oldid=prev 2024-02-14T20:27:24Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←წინა ვერსია</td> <td colspan='2' style="background-color: white; color:black;">20:27, 14 თებერვალი 2024-ის ვერსია</td> </tr><tr><td colspan="2" class="diff-lineno">ხაზი 2:</td> <td colspan="2" class="diff-lineno">ხაზი 2:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>f(x) = f(x&lt;sub&gt;0&lt;/sub&gt;) + f'(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)/1! + f &quot;(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt; )&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt; (x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)&lt;sup&gt;n&lt;/sup&gt;/n! +... სადაც f&lt;sup&gt;(n)&lt;/sup&gt;(x&lt;sub&gt;0&lt;/sub&gt;) არის f(x) ფუნქციის n-ური რიგის წარმოებულის მნიშვნელობა x&lt;sub&gt;0&lt;/sub&gt; წერტილში.&#160; ეს [[ფორმულა]] ბ. ტეილორმა გამოაქვეყნა 1715 წელს. &#160;</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>f(x) = f(x&lt;sub&gt;0&lt;/sub&gt;) + f'(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)/1! + f &quot;(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt; )&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt; (x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)&lt;sup&gt;n&lt;/sup&gt;/n! +... სადაც f&lt;sup&gt;(n)&lt;/sup&gt;(x&lt;sub&gt;0&lt;/sub&gt;) არის f(x) ფუნქციის n-ური რიგის წარმოებულის მნიშვნელობა x&lt;sub&gt;0&lt;/sub&gt; წერტილში.&#160; ეს [[ფორმულა]] ბ. ტეილორმა გამოაქვეყნა 1715 წელს. &#160;</div></td></tr> <tr><td colspan="2">&#160;</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;"></ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>როცა x&lt;sub&gt;0&lt;/sub&gt;=0, ფუნქციის ტეილორის მწკრივად გაშლის ფორმულას აქვს შემდეგი სახე:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>როცა x&lt;sub&gt;0&lt;/sub&gt;=0, ფუნქციის ტეილორის მწკრივად გაშლის ფორმულას აქვს შემდეგი სახე:</div></td></tr> </table>

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<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr valign='top'> <td colspan='2' style="background-color: white; color:black;">←წინა ვერსია</td> <td colspan='2' style="background-color: white; color:black;">20:27, 14 თებერვალი 2024-ის ვერსია</td> </tr><tr><td colspan="2" class="diff-lineno">ხაზი 5:</td> <td colspan="2" class="diff-lineno">ხაზი 5:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>როცა x&lt;sub&gt;0&lt;/sub&gt;=0, ფუნქციის ტეილორის მწკრივად გაშლის ფორმულას აქვს შემდეგი სახე:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>როცა x&lt;sub&gt;0&lt;/sub&gt;=0, ფუნქციის ტეილორის მწკრივად გაშლის ფორმულას აქვს შემდეგი სახე:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</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>f(x) = f(0) + f'(0) x /1! + f&quot;(0) x&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt;(0) x&lt;sup&gt;n&lt;/sup&gt;/n! +...</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:::</ins>f(x) = f(0) + f'(0) x /1! + f&quot;(0) x&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt;(0) x&lt;sup&gt;n&lt;/sup&gt;/n! +...</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>კერძოდ:</div></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"><div>კერძოდ:</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</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>(1 + x)&lt;sup&gt;m&lt;/sup&gt; = 1+mx+...+m(m-1)(m-2)... (m-n+1) x&lt;sup&gt;n&lt;/sup&gt; /n! + .. &#160;</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:::</ins>(1 + x)&lt;sup&gt;m&lt;/sup&gt; = 1+mx+...+m(m-1)(m-2)... (m-n+1) x&lt;sup&gt;n&lt;/sup&gt; /n! + .. &#160;</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>e&lt;sup&gt;x&lt;/sup&gt; = 1 + x/1! + x&lt;sup&gt;2&lt;/sup&gt;/2! + x&lt;sup&gt;3&lt;/sup&gt;/3! +… +x&lt;sup&gt;n&lt;/sup&gt; /n! + . . .</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:::</ins>e&lt;sup&gt;x&lt;/sup&gt; = 1 + x/1! + x&lt;sup&gt;2&lt;/sup&gt;/2! + x&lt;sup&gt;3&lt;/sup&gt;/3! +… +x&lt;sup&gt;n&lt;/sup&gt; /n! + . . .</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>sinx = x = x&lt;sup&gt;3&lt;/sup&gt; / 3! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n+1&lt;/sup&gt;/(2n+1)! + . . .</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:::</ins>sinx = x = x&lt;sup&gt;3&lt;/sup&gt; / 3! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n+1&lt;/sup&gt;/(2n+1)! + . . .</div></td></tr> <tr><td class='diff-marker'>−</td><td style="background: #ffa; color:black; font-size: smaller;"><div>cosx = 1-x&lt;sup&gt;2&lt;/sup&gt;/2! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n&lt;/sup&gt; / (2n)! +&#160; . . .</div></td><td class='diff-marker'>+</td><td style="background: #cfc; color:black; font-size: smaller;"><div><ins class="diffchange diffchange-inline">:::</ins>cosx = 1-x&lt;sup&gt;2&lt;/sup&gt;/2! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n&lt;/sup&gt; / (2n)! +&#160; . . .</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td><td class='diff-marker'>&#160;</td><td style="background: #eee; color:black; font-size: smaller;"></td></tr> </table>

Echelidze https://www.nplg.gov.ge/wikidict/index.php?title=%E1%83%A2%E1%83%94%E1%83%98%E1%83%9A%E1%83%9D%E1%83%A0%E1%83%98%E1%83%A1_%E1%83%9B%E1%83%AC%E1%83%99%E1%83%A0%E1%83%98%E1%83%95%E1%83%98&diff=219154&oldid=prev 2024-02-14T20:26:25Z

<p>ახალი გვერდი: &#039;&#039;&#039;ტეილორის მწკრივი&#039;&#039;&#039; – <a href="/wikidict/index.php/%E1%83%AE%E1%83%90%E1%83%A0%E1%83%98%E1%83%A1%E1%83%AE%E1%83%9D%E1%83%95%E1%83%90%E1%83%9C%E1%83%98_%E1%83%9B%E1%83%AC%E1%83%99%E1%83%A0%E1%83%98%E1%83%95%E1%83%98" title="ხარისხოვანი მწკრივი">ხარისხოვანი მწკრივი</a>, რომელზეც შეიძლ...</p> <p><b>ახალი გვერდი</b></p><div>'''ტეილორის მწკრივი''' – [[ხარისხოვანი მწკრივი]], რომელზეც შეიძლება გაიშალოს ნებისმიერი f(x) [[ფუნქცია (მათემატიკური)|ფუნქცია]], თუ ამ ფუნქციას x&lt;sub&gt;0&lt;/sub&gt; [[წერტილი (გეომეტრია)|წერტილზე]] აქვს ყველა რიგის [[წარმოებული]]; ამ [[მწკრივი (მათემატიკა)|მწკრივს]] აქვს ასეთი სახე:<br /> <br /> f(x) = f(x&lt;sub&gt;0&lt;/sub&gt;) + f'(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)/1! + f &quot;(x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt; )&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt; (x&lt;sub&gt;0&lt;/sub&gt;)(x-x&lt;sub&gt;0&lt;/sub&gt;)&lt;sup&gt;n&lt;/sup&gt;/n! +... სადაც f&lt;sup&gt;(n)&lt;/sup&gt;(x&lt;sub&gt;0&lt;/sub&gt;) არის f(x) ფუნქციის n-ური რიგის წარმოებულის მნიშვნელობა x&lt;sub&gt;0&lt;/sub&gt; წერტილში. ეს [[ფორმულა]] ბ. ტეილორმა გამოაქვეყნა 1715 წელს. <br /> <br /> როცა x&lt;sub&gt;0&lt;/sub&gt;=0, ფუნქციის ტეილორის მწკრივად გაშლის ფორმულას აქვს შემდეგი სახე:<br /> <br /> f(x) = f(0) + f'(0) x /1! + f&quot;(0) x&lt;sup&gt;2&lt;/sup&gt;/2! +...+ f&lt;sup&gt;(n)&lt;/sup&gt;(0) x&lt;sup&gt;n&lt;/sup&gt;/n! +...<br /> <br /> კერძოდ:<br /> <br /> (1 + x)&lt;sup&gt;m&lt;/sup&gt; = 1+mx+...+m(m-1)(m-2)... (m-n+1) x&lt;sup&gt;n&lt;/sup&gt; /n! + .. <br /> e&lt;sup&gt;x&lt;/sup&gt; = 1 + x/1! + x&lt;sup&gt;2&lt;/sup&gt;/2! + x&lt;sup&gt;3&lt;/sup&gt;/3! +… +x&lt;sup&gt;n&lt;/sup&gt; /n! + . . .<br /> sinx = x = x&lt;sup&gt;3&lt;/sup&gt; / 3! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n+1&lt;/sup&gt;/(2n+1)! + . . .<br /> cosx = 1-x&lt;sup&gt;2&lt;/sup&gt;/2! + ... + (-1)&lt;sup&gt;n&lt;/sup&gt; x&lt;sup&gt;2n&lt;/sup&gt; / (2n)! + . . .<br /> <br /> <br /> ==წყარო==<br /> [[მათემატიკის ენციკლოპედიური ლექსიკონი]]<br /> <br /> [[კატეგორია:მათემატიკა]]</div>

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