lim t→2 (2t^2−3t−2)/(t^2+t−6)

$\lim \limits_{t\to 2} { \frac{2t^2-3t-2}{t^2+t-6} }$

l'Hospital's rule

$\begin{array}{rcll} \lim \limits_{t\to 2} { \frac{2t^2-3t-2}{t^2+t-6} } &=& \lim \limits_{x\to 2} { \frac{2\cdot 2\cdot t-3}{2\cdot t + 1} }\\ &=& \frac{2\cdot 2\cdot 2-3}{2\cdot 2 + 1}\\ &=& \frac{5}{5}\\ \mathbf{\lim \limits_{t\to 2} { \frac{2t^2-3t-2}{t^2+t-6} } }&\mathbf{=}& \mathbf{1}\\ \end{array}$