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