Answer
$-5$
Work Step by Step
$\lim _{t\rightarrow 2}\dfrac {3t^{2}-7t+2}{2-t}=\dfrac {3t^{2}-6t-t+2}{2-t}=\dfrac {3t\left( t-2\right) -\left( t-2\right) }{2-t}=\dfrac {\left( t-2\right) \left( 3t-1\right) }{-\left( t-2\right) }=-\left( 3t-1\right) =-\left( 3\times 2-1\right) =-5$
