Examples of mathinhtml output

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  1. The derivative of h(x)= {5 \over x} + 4 x^2 is given by h'(x) = \lim_{h \to 0} {-5 \over x^2 + x h} + 8 x + 4 h = {-5 \over x^2} + 8 x.

  2. The derivative of x \sin x \over x^2 + 1 is given by (x^2 + 1)(x \cos x + \sin x) - (x \sin x)(2 x) \over (x^2+1)^2.

  3. The derivative of \sqrt{3 x + 4 x^2 + 5} is given by 3 + 8 x \over 2 \sqrt{3 x + 4 x^2 + 5}.

  4. The derivative of (\sin x)^{\cos x} is given by (\sin x)^{\cos x} \left[{\cos^2 x \over \sin x} - (\sin x) \ln(\sin x)\right] .

  5. \lim_{x \to 1} {\ln(2x - 1) \over \sqrt x - 1} = 4.

  6. The graph of y = {x^3 \over x - 4} is
    set ytics 100; plot [-18:13][-200:300] x**3 / (x-4)

  7. The graph of y = x^4 - a x^3 (for a>0) is
    set xtics("a/2" 0.5, "a" 1); set ytics("-0.1a^4" -0.1,"0.1a^4" 0.1); plot [-0.45:1.1] x**4-x**3