Question

1. $lim_{t

ightarrow - 2}\frac{\frac{1}{2}+\frac{1}{t}}{2 + t}$ *hint: we did a similar one like this on the notes see if you can at least set it up

Explanation:

Step1: Combine the fractions in the numerator

First, find a common - denominator for $\frac{1}{2}+\frac{1}{t}$. The common denominator is $2t$. So, $\frac{1}{2}+\frac{1}{t}=\frac{t + 2}{2t}$.
The original limit becomes $\lim_{t
ightarrow - 2}\frac{\frac{t + 2}{2t}}{2 + t}=\lim_{t
ightarrow - 2}\frac{t + 2}{2t(2 + t)}$.

Step2: Simplify the rational function

Cancel out the common factor $(t + 2)$ in the numerator and the denominator (since $t
eq - 2$ when taking the limit). We get $\lim_{t
ightarrow - 2}\frac{1}{2t}$.

Step3: Evaluate the limit

Substitute $t=-2$ into $\frac{1}{2t}$. We have $\frac{1}{2\times(-2)}=-\frac{1}{4}$.

Answer:

$-\frac{1}{4}$