(ii) To find the distance \(AB\), use the distance formula:

\(AB^2 = \left(3/2\right)^2 + \left(3/4\right)^2\)

\(AB = \sqrt{\frac{45}{4}} \approx 1.68\)

(iii) To find the area of the shaded region, calculate the area under the curve \(y = 2x + (x+1)^{-2}\) from \(x = -\frac{1}{2}\) to \(x = 1\).

The area under the curve is:

\(\int_{-1/2}^{1} \left( x^2 - (x+1)^{-1} \right) \, dx = \left[ \frac{1}{4}x^2 + \frac{11}{4}x \right]_{-1/2}^{1} - \left[ x^2 - (x+1)^{-1} \right]_{-1/2}^{1}\)

Apply limits \(-\frac{1}{2} \to 1\) to both integrals:

\(= \frac{27}{16} \approx 1.69\)