kim

To evaluate the limit \(\lim_{{x \to \infty}} \frac{4x^2 - x}{8x}\), follow these steps:

1. Simplify the expression: \[ \frac{4x^2 - x}{8x} = \frac{4x^2}{8x} - \frac{x}{8x} = \frac{1}{2}x - \frac{1}{8} \]

2. As \(x\) approaches infinity, the dominant term is \(\frac{1}{2}x\), which goes to infinity.

Therefore, the limit is \(\infty\).