The repetitions are the result of pasting from certain web sites that provide both a formatted and an unformatted version of each piece of math. When...
Awesome, looks like I got it from your advice. My simplified form of: x^cos(x^2) * cos (x^(cos(x^2))) (cos(x^2)/x - 2xlnxsin(x^2)) looks better to me...
Don't miss the fact that sqrt(1-sin^2(x^(cos(x^2)))) = cos(x^(cos(x^2))), since in general sqrt(1-sin^2(u)) = cos(u), given that u is in the first or...
To avoid subscripts let a=p_0,~b=p_1,~x=q_0,~y=q_1 now we have:
\begin{array}{l} \dfrac{a}{x} < \frac{b}{y}\\ ay < bx\\ ay + by < bx + by\\ (a + b)y...