Problem Teachers' Notes Hint Solution

Mind Your Ps and Qs

$x^3> 1 \Leftrightarrow x> 1$

$2\int^{x^2}_0ydy> x^2 \Leftrightarrow |x|> 1$

$x=-2 \Leftrightarrow x^2+4x+4 =0$

$x=1\Rightarrow x^2+x-2=0$

$0< x< 1 \Rightarrow \cos(x/2)> \sin(x/2)$

$x> 4\Rightarrow x> 2$

$x< 0 \Leftrightarrow x\int^x_0 ydy < 0$

$x=0 \Rightarrow \int^x_0 \cos y dy =0$