Determine the order, (Oleft(x^{p} ight)), of the following functions. You may need to use series expansions in

Determine the order, \(O\left(x^{p}\right)\), of the following functions. You may need to use series expansions in powers of \(x\) when \(x \rightarrow 0\), or series expansions in powers of \(1 / x\) when \(x \rightarrow \infty\).

a. \(\sqrt{x(1-x)}\) as \(x \rightarrow 0\).

b. \(\frac{x^{5 / 4}}{1-\cos x}\) as \(x \rightarrow 0\).

c. \(\frac{x}{x^{2}-1}\) as \(x \rightarrow \infty\).

d. \(\sqrt{x^{2}+x}-x\) as \(x \rightarrow \infty\).