The side of a square is increased from $3cm \mathrm{to} 3.01cm$. Find the approximate increase in the area of the square.

Let $x$ be the side of the square, $A$ be the area given $x=3$ and $\mathrm{\Delta }x=0.01$

Area $A=x^2$

Approximate increase in area of the square is 

$\mathrm{\Delta }A=2x\mathrm{\Delta }x\Rightarrow \mathrm{\Delta }A=2\left(3\right)\left(0.01\right)\Rightarrow \mathrm{\Delta }A=0.06$