Answer
a) $0$
b) $-6$
Work Step by Step
a) Divide $\frac{2 + 3t}{5t^2 + 6}$ with $t^2$ in both numerator and denominator. We get
$\frac{\frac{2}{t^2} + \frac{3}{t}}{5 + \frac{6}{t^2}}$
Then apply $\lim\limits_{t \to -\infty}$.
$\displaystyle\lim_{t\rightarrow-\infty}\frac{\frac{2}{t^2} + \frac{3}{t}}{5 + \frac{6}{t^2}}=\frac{0+0}{5+0}=0$
because the limits of $\frac{2}{t^2}$ ,$\frac{3}{t}$ , $\frac{6}{t^2}$ are $0$.
b) Take $\frac{\sqrt{36t^2 - 100}}{5-t}$ , Divide by $t$ in both numerator and denominator.
We get $\frac{\sqrt{36 - \frac{100}{t^2}}}{\frac{5}{t}-1}$
Applying $\lim\limits_{t \to +\infty}$ we get
$\displaystyle\lim_{t\rightarrow-\infty}\frac{\sqrt{36 - \frac{100}{t^2}}}{\frac{5}{t}-1}=\frac{6}{-1}=-6$
