Calculating limits at infinity might look hard at first, but it gets easier once you learn some simple methods. Here are some helpful ways to find limits:

1. Direct Substitution: If you can, just plug in infinity for $x$ in the function. For instance, if you have a function like $\frac{3x^2 + 5}{2x^2 - 4}$, when you substitute $x = \infty$, you get $\frac{3(\infty)^2 + 5}{2(\infty)^2 - 4}$. This simplifies to $\frac{3\infty^2}{2\infty^2}$, and in the end, the limit is $\frac{3}{2}$.

2. Factor and Simplify: When you're working with polynomials, take out the highest power of $x$ from both the top and bottom of the fraction. For example, in $\frac{x^3 + 3x^2 - 2}{2x^3 + x + 1}$, you can factor out $x^3$: $\frac{x^3(1 + \frac{3}{x} - \frac{2}{x^3})}{x^3(2 + \frac{1}{x^2} + \frac{1}{x^3})}$ As $x$ approaches infinity, the limit becomes $\frac{1}{2}$.

3. L'Hôpital's Rule: This rule is very helpful when you see forms like $\frac{\infty}{\infty}$. Just take the derivative (which means finding the slope) of the top and bottom until you can directly find the limit.

4. Dominance of Terms: For rational functions, the biggest terms matter most as $x$ goes to infinity. So, you can focus on these highest degree terms to find the limit easily.

All these methods can really help, depending on the limit problem you have. Just keep practicing, and you’ll find out which method works best in different situations!