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Chapter 3 Another Chapter

3.1 Generating Theorem Environments Using Pandoc Fence Code Blocks

Bookdown has a lua filter called “latex-div.lua” which handles theorem environments for latex.

If \(c\) denotes the length of the hypotenuse and \(a\) and \(b\) denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: \[a^2+b^2=c^2.\]

If \(c\) denotes the length of the hypotenuse and \(a\) and \(b\) denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: \[a^2+b^2=c^2.\]

If \(c\) denotes the length of the hypotenuse and \(a\) and \(b\) denote the lengths of the other two sides, the Pythagorean theorem can be expressed as the Pythagorean equation: \[a^2+b^2=c^2.\]

For any angle \(\theta\), we have \[ \sin^2\theta+\cos^2\theta=1 \]

For any angle \(\theta\), we have \[ \sin^2\theta+\cos^2\theta=1 \]

For any angle \(\theta\), we have \[ \sin^2\theta+\cos^2\theta=1 \]

By ??, we know that …. ??

Pandoc use ::: {#Id .Div_attributes} to start and ::: to end a Div block. Such a block can be converted to LaTeX environment using lua.

Let \(f\) be a function differentiable over \((a, b)\). If \(f'(x)>0\) for any \(x\) in \((a, b)\), then \(f(a)<f(x)<f(b)\)$ for any \(x\) in \((a,b)\).

Find the hypotenuose for the right triangle whose legs are 4 and 3.

By ??, the hypothenuose is \[ \sqrt{3^2+4^2}=5. \]

3.2 Practice

Simplify. Write with positive exponents.

1. \((3a^2b^3c^2)(4abc^2)(2b^2c^3)\)
2. \(\dfrac{4y^3z^0}{x^2y^2}\)
3. \((-2)^{-3}\)