give me limit property problems and say if I'm correct

Sure! Here are some limit property problems for you to solve. After each one, I’ll let you know if your answer is correct.

### Problem 1:
\[
\lim_{x \to 3} (2x + 5)
\]

### Problem 2:
\[
\lim_{x \to 0} (x^2 - 4x + 7)
\]

### Problem 3:
\[
\lim_{x \to -2} \frac{x^2 - 4}{x + 2}
\]

### Problem 4:
\[
\lim_{x \to \infty} \frac{5x^3 - 2x + 1}{x^3 + x^2}
\]

### Problem 5:
\[
\lim_{x \to 1} \frac{2x^2 - 3x + 1}{x - 1}
\]

### Problem 6:
\[
\lim_{x \to 0} \frac{\sin(x)}{x}
\]

### Problem 7:
\[
\lim_{x \to \infty} \left( \frac{1}{x} + \frac{2}{x^2} \right)
\]

### Problem 8:
\[
\lim_{x \to 0^+} \ln(x)
\]

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Please solve these problems, and I’ll check your answers for correctness.

Explore a series of limit property problems and check your solutions. Problems include limits approaching specific values, infinity, and the use of differentiation. Suitable for advanced high school students and those preparing for calculus exams.

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