Evaluate $\underset{x→∞}{\lim}\frac{2x^2+2x-\sin^2x}{3x^2-4x+\cos^2x}$.

$\frac{1}{3}$ $\frac{3}{2}$ $\frac{2}{3}$ 3

$\frac{2}{3}$

$\underset{x→∞}{\lim}\frac{2x^2+2x-\sin^2x}{3x^2-4x+\cos^2x}(\frac{→∞}{→∞})$ Divide by highest power of ‘x’ : $\underset{x→∞}{\lim}\frac{\frac{2x^2}{x^2}+\frac{2x}{x^2}-\frac{\sin^2x}{x^2}}{\frac{3x^2}{x^2}-\frac{4x}{x^2}+\frac{\cos^2x}{x}}=\frac{2+0^2-0}{3-0+0^2}=\frac{2}{3}$