Let's go through the mathematical problems in the image you provided. Here is a list of the problems:

1. Evaluate $\lim f(x)$ where $2x - 1 \leq f(x) \leq x^2$ for all $x$ in the interval $(0, 2)$.

2. Find constants $a$ and $b$ such that $\lim_{x \to 10} \frac{\sqrt{ax + b} - 2}{x} = 1$.

3. Is there a number $a$ such that $\lim_{x \to -2} \frac{ax^2 + 15x + 15 + a}{x^2 + x - 2}$ exists? If so, find the value of $a$ and the value of the limit.

4. **Determine the value of (