Answer
1
Work Step by Step
$\lim\limits_{t \to -1}\frac{t^{2}+1}{(t^{3}+2)(t^{4}+1)}=\frac{\lim\limits_{t \to -1}(t^{2}+1)}{\lim\limits_{t \to -1}[(t^{3}+2)(t^{4}+1)]}$ (Quotient Law)
$=\frac{\lim\limits_{t \to -1}(t^{2}+1)}{(\lim\limits_{t \to -1}t^{3}+2)(\lim\limits_{t \to -1}t^{4}+1)}$ (Product Law)
$=\frac{\lim\limits_{t \to -1}t^{2}+\lim\limits_{t \to -1}1}{(\lim\limits_{t \to -1}t^{3}+\lim\limits_{t \to -1}2)(\lim\limits_{t \to -1}t^{4}+\lim\limits_{t \to -1}1)}$ (Sum Law)
$=\frac{1+1}{(-1+2)(1+1)}=1$
