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<h3>The Cauchy-Schwarz Inequality (TeX)</h3>
\[ \left( \sum_{k=1}^n a_k b_k \right)^2 \leq \left( \sum_{k=1}^n a_k^2 \right) \left( \sum_{k=1}^n b_k^2 \right) \]
<h3>Standard Deviation (MathML)</h3>
<math display="block"><mrow><mi>σ</mi><mo>=</mo><msqrt><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac><mstyle displaystyle="true"><mrow><munderover><mrow><mo>∑</mo></mrow><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>N</mi></mrow></munderover><mrow><msup><mrow><mo stretchy="false">(</mo><msub><mrow><mi>x</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>−</mo><mi>μ</mi><mo stretchy="false">)</mo></mrow><mrow><mn>2</mn></mrow></msup></mrow></mrow></mstyle></mrow></msqrt><mo>.</mo></mrow></math>
<h3>Inline equation (TeX)</h3>
<p>Finally, while display equations look good for a page of samples, the ability to mix math and text in a paragraph is also important. This expression \(\sqrt{3x-1}+(1+x)^2\) is an example of an inline equation. As you see, MathJax equations can be used this way as well, without unduly disturbing the spacing between lines.</p>
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<form autocomplete="off" action="MathJaxProcess.php" method="POST" id="pdfform" onSubmit="document.getElementById('bodydata').value=encodeURIComponent(document.body.innerHTML);">
<input type="submit" value="PDF" name="PDF"/>
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