\ANG{
Ermitteln Sie folgende Grenzwerte.
\begin{tabular}[t]{llll}
(a) $\D\lim_{x\to 0}\frac{\sin ax}{\sin bx}$ &
(b) $\D\lim_{x\to a}\frac{\sqrt x - \sqrt a}{x-a}$ &
(c) $\D\lim_{x\to a^{+}}\frac{\sqrt x - \sqrt a}{\sqrt{x-a}}$ &
(d) $\D\lim_{x\to 0}\frac{1-\cos x}{x}$\\
&&&\\
(e) $\D\lim_{x\to 0}\frac{1-\cos x}{x^2}$ &
(f) $\D\lim_{x\to 0^{\pm}}\frac{1-\cos x}{x^3}$ &
(g) $\D\lim_{x\to 0}\frac{\sin x}{x+\sin x}$ &
(h) $\D\lim_{x\to 0}\frac{x^2 \sin \frac{1}{x}}{\sin x}$
\end{tabular}

}
\LSG{
\begin{tabular}[t]{lll}
(a) $\D\frac{a}{b}$ &
(b) $\D\frac{1}{2\,\sqrt a}$ &
(c) $\D\lim_{x\to a^{+}}\frac{\sqrt x - \sqrt a}{\sqrt{x-a}}=
    \begin{cases}
    0 & \text{f"ur $a>0$}\\
    1 & \text{f"ur $a=0$}
    \end{cases}$\\
&&\\
(d) 0 &
(e) $\D\frac{1}{2}$ &
(f) $\D\pm\infty$\\
&&\\
(g) $\D\frac{1}{2}$ &&
(h) $\D\lim_{x\to 0}\frac{x \sin \frac{1}{x}}{\frac{\sin x}{x}}=0$ 
    (de l'Hospital funktioniert nicht)
\end{tabular}
}
