From 9bd5acdfccade3096e5c588f7864a49e89a48020 Mon Sep 17 00:00:00 2001 From: Miguel Buenache Date: Tue, 23 Oct 2018 18:08:13 +0200 Subject: [PATCH] exescises --- exercise-02-plik.pdf | Bin 0 -> 54730 bytes exercise-02-plik.tex | 63 +++++++++++++++++++++++++++++++++++++++++++ 2 files changed, 63 insertions(+) create mode 100644 exercise-02-plik.pdf create mode 100644 exercise-02-plik.tex diff --git a/exercise-02-plik.pdf b/exercise-02-plik.pdf new file mode 100644 index 0000000000000000000000000000000000000000..929bdd8a36570a4d9b86523eb9aef3af7d1d4091 GIT binary patch literal 54730 zcma&NQ>-vRyJop<+qP}nwr$(CZR^{%ZQHhOqyL%A>FK1;#i^@$Z!4+P%6jS{RS*%Q zWu#+;BAs6zS%+dKU?8wJvV!8_fuff&wKI3IAYfu*;vo2c7ZkmirHzZJ69K)LjiHOF zh^eu?i76BxAC$9;lc}LCl*i_drgZXlD`M|moq=6W6vPp%5i0JXdZ`X4$7?5*Y8pIB zq^{zj@i5^{>f_mxheKG#$aO6et`a9ANLK8v*xTC9{u;ZwzOTGUSz?-s8G9S%0gxpf zQz$BtiV3^ytF_#GEds_Fzub|Z`aBc6@|&YNL+Fzycpd)G^}w`S+VPY2QM&zDEjH~0 z{*A-g+GWFCRpGjb&8by>eT-cJ)OcC&Csc&uO72O%*EWg2P-0d3HHQ%C;I zruv?8ucCsHNC}8i+_BWByu7#zS)y8XvrDLmRC09zh@ysri*122rg$gG^rE85pi^Mt zDw78FKx|W(s z1exekl!-@^y4pJ@L!iQ=)cSIJO~yB+93=PQr#H~i3u=Ky>bJoce;^T@qE-I>EB

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+\begin{document} + +\begin{enumerate} + +\newtheorem{thm}{Theorem} + +\newtheorem{df}{Definition} + +\item Properly typeset the following command and properly refere to it in the text +\begin{align*} +&\sum_{i_1,\dots,i_m} a_{i_1,\dots,i_m}^{2m}{m+1} {\frac{m+1}{2m}} \leq \\ +C \sup\Big\{ |&\sum_{i_1,\dots, i_m} a_{i_1,\dots,i_m} x^1_{i_1}\dots x^m_{i_m}|: \|(x_i^k)_{i=1}^n \|_\infty\leq1,\ 1\leq k\leq m\Big\}, +\end{align*} +\item Properly typset the expression: $\operatorname{Re} z$. + +\item Properly typeset indexes in the following sum: +\[ +f(x)=\sum_{\substack{n=0\\ k=2}}^\infty a_n^k +\] +\item Properly typeset the following theorem +\begin{thm}[Cauchy--Hadamard] + \emph{The radius of convergence $R$ of the power series} +\[ +\sum_{n=0}^\infty a_n(z-z_0)^n,\ \ \ \ \ |z-z_0|