\( \frac { \lim ( x ^ { 2 } - 3 x + 5 ) } { x 2 } \)

To solve \( \frac{\lim_{x \to a} (x^2 - 3x + 5)}{x^2} \), we first need to clarify the limit's behavior as \( x \) approaches a specific value. Let's say we look at the limit as \( x \to 0 \) for simplicity. Plugging \( x = 0 \) into the numerator gives us \( 0^2 - 3(0) + 5 = 5 \). The denominator \( x^2 \) at \( x = 0 \) is also \( 0 \), which creates a \( \frac{5}{0} \) scenario. This indicates that the expression approaches infinity, pointing to a vertical asymptote at \( x = 0 \). For more complex approaches, one could apply L'Hôpital's Rule if both the numerator and denominator yield \( 0 \) or \( \pm \infty \), but in our simple example, this isn't necessary! Just remember when evaluating limits involving quadratics and polynomials, the key is the behavior as \( x \) approaches your target value.