Find two positive numbers whose sum is 12 and their product is maximum.

The volume of a cylinder is given by the formula V = πr² h. Find the greatest and least values of V if r + h = 6.

Evaluate the following limit, if necessary use l ’Hôpital Rule
\(\underset { x\rightarrow \infty }{ lim } \frac { x }{ logx } \) 

Evaluate the following limit, if necessary use  l ’Hôpital Rule
\(\underset { x\rightarrow \frac { { \pi }^{ - } }{ 2 } }{ lim } \frac { secx }{ tanx } \)

Prove that the function f (x) = x² − 2x − 3 is strictly increasing in \((2, \infty)\)