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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

Evaluate each of the given limits:
1. \( \lim_{{t \to +\infty}} \frac{1}{3} t^2 \)
2. \( \lim_{{t \to +\infty}} (3e^t - 7) \)
3. \( \lim_{{t \to -\infty}} \ln(7 - 3t) \)
4. \( \lim_{{t \to 0}} \ln(-3t) \)
5. \( \lim_{{t \to 7/3}} \ln(3t - 7) \)
6. \( \lim_{{t \to 7/3}} \ln(7 - 3t) \)
7. \( \lim_{{t \to -\infty}} -\frac{1}{3} t^2 \)
8. \( \lim_{{t \to +\infty}} -3t \)
9. \( \lim_{{t \to +\infty}} -\frac{1}{3} t^2 \)
10. \( \lim_{{t \to -\infty}} \ln(-3t) \)

Detailed solution for evaluating a variety of limits involving polynomial, exponential, and logarithmic functions as t approaches infinity, zero, or specific values. Covers properties of limits, exponential growth, and natural logarithms. Suitable for Grades 11-12 and college-level students.

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