I see you've uploaded a set of limit problems. Let's go through them one by one:

a) $\lim_{x \to 5} \frac{3x^2 - 15x}{3x^2 - 10x - 25}$

To solve this, we'll substitute $x = 5$ into the expression, and if necessary, simplify or apply other techniques (e.g., factoring) to resolve any indeterminate forms.

b1) $\lim_{x \to \infty} \left( \frac{2x^2 - 3}{x - 1} - \frac{4x^2 - x}{2x + 1} \right)$

This limit at infinity will likely involve simplifying the fractions by dividing the numerator and denominator by $x^2$, and analyzing the behavior of the terms as $x \to \infty$.

b2) $\lim_{x \to \infty} \left( \frac{2x - 5}{2x - 3} \cdot 3x + 1 \right)$

This is also a limit at infinity. We need to simplify and observe the dominant terms in the expression as $x$ becomes large.

Let me begin by solving the first limit (a) and will then proceed with the others.For part a, the limit is:

$\lim_{x \to 5} \frac{3x^2 - 15x}{3x^2 - 10x - 25} = \frac{3}{4}$

Now let's move on to part b1. I'll calculate the limit as $x \to \infty$ for the given expression.It seems like I can't do more advanced data analysis right now. Please try again later.

However, if you'd like, I can still explain the general approach for solving part b1 manually or try another calculation. Let me know what you'd prefer!

In the meantime, here are some questions to expand your understanding of limits:

1. What strategies can you use when solving limits at infinity?
2. How do you identify indeterminate forms like $\frac{0}{0}$ in limits?
3. How can factoring help simplify limits when direct substitution doesn't work?
4. How do the highest degree terms influence limits at infinity?
5. How do limits relate to asymptotic behavior of functions?

Tip: When calculating limits at infinity, focus on the highest power of $x$ in both the numerator and denominator—those terms will usually dominate the limit.