\[1)\ f(x) = \left\{ \begin{matrix} 1 - x^{2}\ при\ x < 2 \\ 3x - 9\ при\ x \geq 2 \\ \end{matrix} \right.\ \text{\ \ \ }\]
\[a = 2;\]
\[\lim_{\begin{matrix} x \rightarrow 2 \\ x < 2 \\ \end{matrix}}\left( 1 - x^{2} \right) = 1 - 4 = - 3;\]
\[\lim_{\begin{matrix} x \rightarrow 2 \\ x > 2 \\ \end{matrix}}(3x - 9) = 6 - 9 = - 3.\]
\[Что\ и\ требовалось\ доказать.\]
\[2)\ f(x) = \left\{ \begin{matrix} \left| \cos x \right|\text{\ \ \ \ \ \ \ \ \ \ \ \ \ }при\ x < \pi \\ (x - \pi)^{2} + 1\ при\ x \geq \pi \\ \end{matrix} \right.\ \ \]
\[a = \pi;\]
\[\lim_{\begin{matrix} x \rightarrow \pi \\ x < \pi \\ \end{matrix}}\left| \cos x \right| = \left| \cos\pi \right| = | - 1| = 1;\]
\[\lim_{\begin{matrix} x \rightarrow \pi \\ x > \pi \\ \end{matrix}}\left( (x - \pi)^{2} + 1 \right) = 0 + 1 = 1.\]
\[Что\ и\ требовалось\ доказать.\]