Question

Below the pink line is the answer, make sure to explain why

Answer 1

`-5`

Step-by-step explanation:

Here, we want to find the limit shown

To do this, we start by factorizing the numerator

Thus, we have that as:

`\begin{gathered} 3t^2-7t\text{ + 2 = 3t}^2-6t-t+2 \\ =\text{ 3t\lparen t-2\rparen-1\lparen t-2\rparen = \lparen3t-1\rparen\lparen t-2\rparen} \end{gathered}`

Now, from here, we have the original fraction reduced to the following:

`\begin{gathered} (3t^2-7t+2)/(2-t)\text{ = }((3t-1)(t-2))/(2-t)\text{ = }(-(2-t)(3t-1))/(2-t) \\ \\ =\text{ -\lparen3t-1\rparen = 1-3t} \end{gathered}`

Finally, we find the limit as follows:

`\lim_(t\to2)\text{ }(3t^2-7t+2)/(t-2)\text{ = }\lim_(t\to2)\text{ 1-3t = 1-3\lparen2\rparen = 1-6 = -5}`