Find the limit as x approaches infinity of (3x^2 + 2x)/(5x^2 - 1)

Problem: Find the limit $\lim_{x \to \infty} \frac{3x^2 + 2x}{5x^2 - 1}$.

Steps

1. Divide numerator and denominator by highest power of x
   $$\lim_{x \to \infty} \frac{\frac{3x^2}{x^2} + \frac{2x}{x^2}}{\frac{5x^2}{x^2} - \frac{1}{x^2}}$$
2. Simplify the fractions
   $$\lim_{x \to \infty} \frac{3 + \frac{2}{x}}{5 - \frac{1}{x^2}}$$
3. Apply the limit as x approaches infinity
   $$\frac{3 + 0}{5 - 0}$$
4. Simplify the result
   $$\frac{3}{5}$$