$(33$ pts in total$)$ Strictly prove the following Little Oh asymptotic notations using the second

definition discussed in class.

$x=o(x^2)(3pts)$

$x=o(x^2-x)(3pts)$

$x=o(x^2+x)(4pts)$

$x=o(x^2-7)(3pts)$

$x=o(x^2+7)(4pts)$

$x=o(x^3+10)(8pts)$

$500\sqrt[\phantom{2}]{x}=o(x)(8pts)$