Let's go through each limit one by one:

1. $\lim_{{t \to +\infty}} \frac{1}{3} t^2$:

   • As $t \to +\infty$, $t^2$ grows to infinity. Thus, $\frac{1}{3} t^2 \to +\infty$.
   • Answer: $+\infty$

2. $\lim_{{t \to +\infty}} (3e^t - 7)$:

   • As $t \to +\infty$, $e^t$ grows exponentially, so $3e^t$ also goes to infinity. Subtracting a constant $7$ does not change the result.
   • Answer: $+\infty$

3. $\lim_{{t \to -\infty}} \ln(7 - 3t)$:

   • As $t \to -\infty$, $3t$ becomes a large positive value (since $3t$ is negative for large negative $t$), so $7 - 3t$ approaches $+\infty$.
   • The natural logarithm