$${1.Zbadac\ zbieznosc\ \sum_{n = 1}^{\infty}\frac{\left( 2n \right)!4^{n}}{n^{2n}}\backslash n}{2.Asymtota\ pozioma\ prawostronna\ f\left( x \right) = \left( \frac{2}{\pi}\text{arctgx} \right)^{x}\backslash n}{3.Monotonicznosc\ i\ ekstrema\ f\left( x \right) = arctgx - \ln\left( x + 1 \right)\backslash n}{4.Rozwiazac\ w\ zaleznosci\ od\ a\left\{ \begin{matrix} 9x + ay + 5z = 0 \\ 2x + y + 3z = 0 \\ - x + 2y + 7z = 0 \\ \end{matrix} \right.\ \backslash n}{5.\ \int_{}^{}{\frac{x + sinx}{\sin^{2}x}\text{dx}}\backslash n}{6.Punkt\ P\left( 0;7; - 3 \right)i\ prosta\ l:\left\{ \begin{matrix} x = 1 + 2t \\ y = 2 - t \\ z = - 4 + 5t \\ \end{matrix},\ \begin{matrix} a)\ plaszczyzna\ zawierajaca\ P\ i\ l \\ b)\ odleglosc\ P\ od\ l \\ c)\ rzut\ P\ na\ l \\ \end{matrix} \right.\ \backslash n}{7.\text{Odwzorowanie}R^{3} \rightarrow R^{2}\text{\ A}\left( x_{1};x_{2};x_{3} \right) = \left( 2x_{1};x_{2} + x_{3}\ \right),\ czy\ jest\ liniowe\backslash n}{\text{\ \ \ z}najdz\ macierz\ odwzorowania\ dla\ R^{3}:\left\{ \begin{matrix} {\overset{\rightarrow}{u_{1}} = \lbrack 1;2;0\rbrack} \\ \overset{\rightarrow}{u_{2}} = \lbrack 1;1;1\rbrack \\ \overset{\rightarrow}{u_{3}} = \lbrack 0;0;1\rbrack \\ \end{matrix}\text{\ i\ }R^{2} \right.\ :\left\{ \begin{matrix} {\overset{\rightarrow}{u_{1}} = \left\lbrack 0;3 \right\rbrack} \\ \overset{\rightarrow}{u_{2}} = \lbrack - 1;1\rbrack \\ \end{matrix} \right.\ \ }$$