Answer
$\displaystyle \frac{4}{49}$
Work Step by Step
$\displaystyle \lim_{t\rightarrow 2}(\frac{t^{2}-2}{t^{3}-3t+5})^{2}$=
... Law 6, $\displaystyle \lim_{x\rightarrow a}[f(x)]^{n}=[\lim_{x\rightarrow a}f(x)]^{n}$
$=(\displaystyle \lim_{t\rightarrow 2}\frac{t^{2}-2}{t^{3}-3t+5})^{2}$
... Law 5, (quotient)
$=(\displaystyle \frac{\lim_{t\rightarrow 2}(t^{2}-2)}{\lim_{t\rightarrow 2}(t^{3}-3t+5)})^{2}$
...Laws 1 (sum), 2 (difference), and 3 (constant multiple)
$=(\displaystyle \frac{\lim_{t\rightarrow 2}t^{2}-\lim_{t\rightarrow 2}2}{\lim_{t\rightarrow 2}t^{3}-3\lim_{t\rightarrow 2}t+\lim_{t\rightarrow 2}5})^{2}$
... Laws 9: $( \displaystyle \lim_{x\rightarrow a}x^{n}=a^{n})$,7:($\displaystyle \lim_{x\rightarrow a}c=c$), and 8: ( $\displaystyle \lim_{x\rightarrow a}x=a$)
$=(\displaystyle \frac{4-2}{8-3(2)+5})^{2}$
$=(\displaystyle \frac{2}{7})^{2}$
$=\displaystyle \frac{4}{49}$
