a) \( \int \frac{\sin x \cos x}{\sin ^{2} x-3 \sin x+2} d x \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l | } { x } & { - 0.001 } & { 0 } & { 0.001 } \\ \hline F ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

4. For which values of \( x \) will \( \sum_{k=1}^{\infty}(4 x-1)^{k} \) exists.

\( \begin{array} { l } { \lim _ { x \rightarrow 3 } ( \frac { x - 3 } { x ^ { 2 } - 9 } ) } \\ { x } \\ { x ( x ) } \\ { f ( x ) } \\ { - 2.99 } \end{array} - 2.999 | 3 | 3.001 | 3.01 | ) \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | l | } { x } & { - 0.001 } & { 0 } & { 0.001 } \\ \hline f ( x ) & { } & { } & { } \\ \hline \end{array} \right. } \end{array} \right. \)

\( \left. \begin{array} { l } { \lim _ { x \rightarrow 0 } ( \frac { \sin x } { x } ) } \\ { \left. \begin{array} { l | l | l | } \hline & { - 0.001 } & { 0 } \\ { F ( x ) } & { 0.001 } \\ \hline \end{array} \right. } \end{array} \right. \)