Calculate the following limits by direct substitution.

$\displaystyle{\lim_{t\to 5} \frac{(1-t)(t+5)}{3t-7} =}$

$\displaystyle{\lim_{y\to -2} y^3(5-3y^2) =}$

$\displaystyle{\lim_{y\to -1} (6-y)(y^2+1)^3 =}$

$\displaystyle{\lim_{s\to 8} \sqrt{\frac{13-s}{s+12}}=}$

$\displaystyle{\lim_{a\to -10} \frac{(a+7)^4}{a+1} =}$

$\displaystyle{\lim_{a\to -4} \frac{a^2-3a+4}{a-12} =}$