Faire un développement limité ou asymptotique en \(a\) à l’ordre \(n\) de :
1
\(\ln \cos x\) \(n = 6\) \(a = 0\).
2
\(\dfrac{\arctan x -x}{\sin x -x}\) \(n = 2\) \(a = 0\).
3
\(\ln \tan (\frac x2 + \frac{\pi}4)\) \(n = 3\) \(a = 0\).
4
\(\ln \sin x\) \(n = 3\) \(a = \frac{\pi}4\).
5
\(\sqrt[3]{x^3 + x}-\sqrt[3]{x^3-x}\) \(n = 4\) \(a = + \infty\).
6
\((1 + x)^{\frac 1x}\) \(n = 3\) \(a = 0\).
7
\(x (\sqrt{x^2 + \sqrt{x^4 + 1}}-x\sqrt 2)\) \(n = 2\) \(a = + \infty\).