Answer
$\displaystyle \frac{7}{8}$
Work Step by Step
$\displaystyle \lim_{t\rightarrow-2}\frac{t^{4}-2}{2t^{2}-3t+2}$
...Limit Law 5, limit of a quotient
$=\displaystyle \frac{\lim_{t\rightarrow-2}(t^{4}-2)}{\lim_{t\rightarrow-2}(2t^{2}-3t+2)}$
...1 (sum), 2 (difference), and 3 (constant multiple)
$=\displaystyle \frac{\lim_{t\rightarrow-2}t^{4}-\lim_{t\rightarrow-2}2}{2\lim_{t\rightarrow-2}t^{2}-3\lim_{t\rightarrow-2}t+\lim_{t\rightarrow-2}2} =$
Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$, 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$), and 7:($\displaystyle \lim_{x\rightarrow a}c=c$)
$=\displaystyle \frac{16-2}{2(4)-3(-2)+2}$
$=\displaystyle \frac{14}{16}$
$=\displaystyle \frac{7}{8}$
