\(\lim\limits_{\mathrm x\to \frac{1}{2}}\frac{2\mathrm x^2-5\mathrm x+2}{\sin(4\mathrm x-2)}\) \(\left(\frac{0}{0}\right)\)
\(=\lim\limits_{\mathrm x\to \frac{1}{2}}\frac{4\mathrm x-5}{\cos(4\mathrm x-2)}\) (By D.L.H. Rule)
\(=\frac{4\times \frac{1}{2}-5}{4\cos(4\times \frac{1}{2}-2)}\) \(=\frac{2-5}{4\cos 0}\) \(=\frac{-3}{4}\)
