# How do you use the epsilon delta definition to prove that the limit of x^3+6x^2=32 as x->2?

delta(epsilon)=min(1;epsilon/49)
$\left\mid {x}^{3} + 6 {x}^{2} - 32 \right\mid = \left\mid x - 2 \right\mid {\left(x + 4\right)}^{2}$
abs(x-2) < min(1;epsilon/49) rArr (x+4)^2<(2+1+4)^2=49
$\left\mid {x}^{3} + 6 {x}^{2} - 32 \right\mid < \frac{\epsilon}{49} \cdot 49 = \epsilon$