(i) Express \(f(x)\) as partial fractions:

Assume \(f(x) = \frac{A}{2x+1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}\).

Equating coefficients, we find:

\(A = 1\), \(B = 0\), \(C = 4\).

Thus, \(f(x) = \frac{1}{2x+1} + \frac{4}{(x-2)^2}\).

(ii) For small \(x\), expand \((1 + 2x)^{-1}\) and \((x-2)^{-2}\):

\((1 + 2x)^{-1} \approx 1 - 2x\)

\((x-2)^{-2} \approx 1 + 4x + 8x^2\)

Multiply these expansions:

\((1 - 2x)(1 + 4x + 8x^2) \approx 1 + 2x + 8x^2\)

Combine terms to get:

\(f(x) \approx 1 - x + 5x^2\).