Advertisement
SigmaBoy456

formula math #5882

Feb 3rd, 2025
29
0
Never
Not a member of Pastebin yet? Sign Up, it unlocks many cool features!
text 6.35 KB | None | 0 0
  1. <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">f</mi><mfenced><mrow><mi mathvariant="normal">x</mi><mo>,</mo><mi mathvariant="normal">y</mi><mo>,</mo><mi mathvariant="normal">z</mi></mrow></mfenced><mo>=</mo><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi mathvariant="normal">w</mi><mo>=</mo><mn>1</mn></mrow><mn>26</mn></munderover><mfenced><mrow><mn>7</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>8</mn><mi mathvariant="normal">y</mi><mo>&#x2212;</mo><mn>15</mn><mi mathvariant="normal">y</mi><mo>+</mo><mn>36</mn><mi mathvariant="normal">z</mi><mo>+</mo><mn>20</mn><mi mathvariant="normal">x</mi><mo>+</mo><mn>10</mn><mi mathvariant="normal">y</mi></mrow></mfenced><mspace linebreak="newline"/><mo rspace="0">&#x2207;</mo><mi mathvariant="normal">f</mi><mo>=</mo><mfenced><mrow><mfrac><mrow><mo>&#x2202;</mo><mi mathvariant="normal">f</mi></mrow><mrow><mo>&#x2202;</mo><mi mathvariant="normal">x</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>&#x2202;</mo><mi mathvariant="normal">f</mi></mrow><mrow><mo>&#x2202;</mo><mi mathvariant="normal">y</mi></mrow></mfrac><mo>,</mo><mfrac><mrow><mo>&#x2202;</mo><mi mathvariant="normal">f</mi></mrow><mrow><mo>&#x2202;</mo><mi mathvariant="normal">z</mi></mrow></mfrac></mrow></mfenced><mo>&#x21d2;</mo><mfenced><mrow><mfrac><mo>&#x2202;</mo><mrow><mo>&#x2202;</mo><mi mathvariant="normal">x</mi></mrow></mfrac><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi mathvariant="normal">w</mi><mo>=</mo><mn>1</mn></mrow><mn>26</mn></munderover><mi mathvariant="normal">f</mi><mfenced><mi mathvariant="normal">x</mi></mfenced><mo>,</mo><mfrac><mo>&#x2202;</mo><mrow><mo>&#x2202;</mo><mi mathvariant="normal">y</mi></mrow></mfrac><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi mathvariant="normal">w</mi><mo>=</mo><mn>1</mn></mrow><mn>26</mn></munderover><mi mathvariant="normal">f</mi><mfenced><mi mathvariant="normal">y</mi></mfenced><mo>,</mo><mfrac><mo>&#x2202;</mo><mrow><mo>&#x2202;</mo><mi>z</mi></mrow></mfrac><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi mathvariant="normal">w</mi><mo>=</mo><mn>1</mn></mrow><mn>26</mn></munderover><mi mathvariant="normal">f</mi><mfenced><mi mathvariant="normal">z</mi></mfenced></mrow></mfenced><mspace linebreak="newline"/><mi>&#x3d5;</mi><msup><mi mathvariant="script">L</mi><mn>0</mn></msup><mo>=</mo><msup><mfenced><mrow><munder accentunder='false'><mi>lim</mi><mrow><mi>x</mi><mo lspace="0" rspace="0">&#x2192;</mo><mi>&#x221e;</mi></mrow></munder><mfrac><mrow><mi>&#x3d5;</mi><msup><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>h</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mfenced><mrow><mn>2</mn><mi>h</mi><mo>+</mo><mn>7</mn><mi>h</mi></mrow></mfenced></mrow></mfenced><mn>0</mn></msup><mo>+</mo><msup><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x220f;</mo><mrow><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mn>3</mn></munderover><mfenced><mn>5</mn></mfenced></mrow></mfenced><mn>0</mn></msup><mo>+</mo><msup><mfenced><mfrac><mn>1</mn><mi>&#x3c0;</mi></mfrac></mfenced><mn>0</mn></msup></mrow><mrow><msup><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><msup><mi>e</mi><mi>i</mi></msup><mo>=</mo><mn>1</mn></mrow><mrow><mo rspace="0">&#x2207;</mo><mi>f</mi></mrow></munderover><mn>0</mn></msup><mfenced><mrow><msubsup><mo>&#x222b;</mo><mrow><mo>&#x2212;</mo><mi>&#x221e;</mi></mrow><mrow><mo>+</mo><mi>&#x221e;</mi></mrow></msubsup><mfrac><mn>1</mn><mi>&#x3c0;</mi></mfrac><mi>s</mi><mi>i</mi><mi>n</mi><mfenced><mi>x</mi></mfenced><mi lspace="0.2em" rspace="0">d</mi><mi>x</mi></mrow></mfenced><mo>+</mo><msup><munderover accent='false' accentunder='false'><mo>&#x220f;</mo><mrow><mi>n</mi><mo>=</mo><mn>2</mn></mrow><mn>5</mn></munderover><mn>0</mn></msup><mfenced><mrow><mi>c</mi><mi>o</mi><mi>s</mi><mfenced><mn>30</mn></mfenced></mrow></mfenced><mo>&#x2212;</mo><msup><mi>e</mi><mrow><mo>&#x2212;</mo><mi>i</mi></mrow></msup><mo>+</mo><msup><mi>e</mi><mn>0</mn></msup></mrow></mfrac></mrow></mfenced><mn>0</mn></msup><mo>.</mo><mo>.</mo><mo>.</mo><mspace linebreak="newline"/><msup><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>t</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mfenced><mrow><msqrt><mi>t</mi></msqrt><mfenced><mrow><msubsup><mo>&#x222b;</mo><mn>0</mn><mi>&#x221e;</mi></msubsup><msup><mi>e</mi><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mfenced><mn>30</mn></mfenced></mrow></msup><mi>x</mi><mi lspace="0.2em" rspace="0">d</mi><mi>x</mi></mrow></mfenced><msub><mi>log</mi><mrow><msup><mi>e</mi><mi>i</mi></msup></mrow></msub><mfenced><mrow><mi>ln</mi><mfenced><mfrac><mn>1</mn><mi>&#x3c0;</mi></mfrac></mfenced></mrow></mfenced></mrow></mfenced></mrow></mfenced><mn>0</mn></msup><msup><mfenced><mfenced><mrow><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>h</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mn>1</mn><mfrac><mn>1</mn><mi>&#x3c0;</mi></mfrac></mrow></mfenced><msup><mn>0</mn><mn>0</mn></msup><mfenced><mrow><mi>ln</mi><mfenced><mn>5</mn></mfenced></mrow></mfenced></mrow></mfenced></mfenced><mn>0</mn></msup><mspace linebreak="newline"/><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>l</mi><mo>=</mo><mn>1</mn></mrow><mn>5</mn></munderover><mfenced><mn>1</mn></mfenced></mrow></mfenced><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>r</mi><mo>=</mo><mn>1</mn></mrow><mn>6</mn></munderover><mfenced><mn>5</mn></mfenced></mrow></mfenced><mo>+</mo><msup><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>s</mi><mo>=</mo><mn>1</mn></mrow><mn>20</mn></munderover><mi>&#x393;</mi><mfenced><mfrac><mrow><mi>c</mi><mi>o</mi><mi>s</mi><mfenced><mrow><msup><mi>e</mi><mi>i</mi></msup></mrow></mfenced></mrow><mrow><mi>s</mi><mi>i</mi><mi>n</mi><mfenced><mrow><msup><mi>e</mi><mrow><mo>&#x2212;</mo><mi>i</mi></mrow></msup></mrow></mfenced></mrow></mfrac></mfenced></mrow></mfenced><mn>0</mn></msup><mo>&#x2212;</mo><mfenced><mrow><munderover accent='false' accentunder='false'><mo>&#x2211;</mo><mrow><mi>j</mi><mo>=</mo><mn>1</mn></mrow><mn>7</mn></munderover><mi>&#x393;</mi><mfenced><mrow><mn>3</mn><mi>j</mi><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>+</mo><mfrac><mn>1</mn><mi>&#x3c0;</mi></mfrac></mrow></mfenced></mrow></mfenced></math>
Advertisement
Add Comment
Please, Sign In to add comment
Advertisement