Infinity Math Example 1

Solution

1. 1
   Divide numerator and denominator by the highest power of $x$ in the denominator, $x^2$.
2. 2
   Numerator: $\frac{3x^2 + 5}{x^2} = 3 + \frac{5}{x^2}$. Denominator: $\frac{x^2-1}{x^2} = 1 - \frac{1}{x^2}$.
3. 3
   As $x \to \infty$, $\frac{5}{x^2} \to 0$ and $\frac{1}{x^2} \to 0$.
4. 4
   Limit: $\frac{3 + 0}{1 - 0} = 3$.