Calculer les limites suivantes : \( (m \in \mathbb{R}_+^*) \)

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\[ \begin{array}{lll} L_1 = \lim\limits_{x \to -\infty} \left( \frac{2}{3} \right)^x \qquad & L_2 = \lim\limits_{x \to 0^+} x^{\sqrt{x}} \qquad & L_3 = \lim\limits_{x \to 1} \frac{x^{\sqrt{x}} - 1}{x - 1} \\ \\ L_4 = \lim\limits_{x \to 0^+} (1 - x)^{\frac{1}{x}} & L_5 = \lim\limits_{x \to \left(\frac{\pi}{2}\right)^-} (\tan x)^{\cos x} & L_6 = \lim\limits_{x \to 0^+} (x^2)^{\frac{1}{\ln^2 x}} \\ \\ L_7 = \lim\limits_{x \to +\infty} x^{\frac{1}{x}} & L_8 = \lim\limits_{x \to 0} \left( \frac{1 + \sin x}{1 + x} \right)^{\frac{1}{x}} & L_9 = \lim\limits_{x \to +\infty} \left( \frac{4x + 15}{4x + 7} \right)^x \\ \\ L_{10} = \lim\limits_{x \to 0} (\cos x)^{\frac{1}{x^2}} & L_{11} = \lim\limits_{x \to +\infty} \left( \frac{\ln x}{\ln(x+1)} \right)^{x \ln x} & L_{12} = \lim\limits_{x \to +\infty} \left( \frac{x}{x - m} \right)^x \\ \\ L_{13} = \lim\limits_{x \to 1^+} \frac{x^x - x}{\ln(1 + \sqrt{x^2 - 1})} & L_{14} = \lim\limits_{x \to +\infty} x \left[ \left( m + \frac{1}{x} \right)^{\frac{1}{x}} - 1 \right] & \end{array} \]