1\documentclass[a4paper,11pt,landscape]{article}
2\usepackage[a4paper,margin=1.4cm,landscape]{geometry}
3\usepackage[T1]{fontenc}
4\usepackage[utf8]{inputenc}
5\usepackage[english]{babel} % change to french
6\usepackage{lmodern}
7\usepackage{amsmath}
8\usepackage{amsfonts}
9\usepackage{amssymb}
10\usepackage{amsthm}
11\usepackage{graphicx}
12\usepackage{color}
13\usepackage{xcolor}
14\usepackage{url}
15\usepackage{theorem}
16\usepackage{textcomp}
17\usepackage{listings}
18\usepackage{hyperref}
19\usepackage{parskip}
20\usepackage{float}
21\usepackage{makecell}
22\usepackage{pgfplots}
23\usepackage{adjustbox}
24
25%\title{DL Usuels}
26%\author{Louis Dalibard}
27%\date{\today}
28
29\begin{document}
30\pagebreak
31\hspace{0pt}
32\vfill
33\begin{table}
34\centering\setcellgapes{1pt}\makegapedcells
35\makebox[\linewidth]{
36 \begin{tabular}{!{\qquad}l|l!{\qquad}} \Xhline{2\arrayrulewidth}
37 \hline
38 A l'ordre $n$ & Premiers termes \\ \hline
39 $\cos(x) = \sum\limits_{k=0}^{n}(-1)^k\frac{x^{2k}}{(2k)!}+o_{x \rightarrow 0}(x^{2n+1}) $ & \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\cos(x)$ & $=$ & $1$ & $-$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^4}{24}$ & $+$ & $o_{x \rightarrow 0}(x^5)$ \\
40 & & \begin{tikzpicture}[scale=0.3, transform shape]
41 \begin{axis}[domain=-2:2,legend pos=outer north east]
42 \addplot[color=red] {cos(deg(x))};
43 \addplot[color=blue] {1};
44 \end{axis}
45 \end{tikzpicture}
46 & & \begin{tikzpicture}[scale=0.3, transform shape]
47 \begin{axis}[domain=-2:2,legend pos=outer north east]
48 \addplot[color=red] {cos(deg(x))};
49 \addplot[color=blue] {1-x^2/2)};
50 \end{axis}
51 \end{tikzpicture}
52 & & \begin{tikzpicture}[scale=0.3, transform shape]
53 \begin{axis}[domain=-2:2,legend pos=outer north east]
54 \addplot[color=red] {cos(deg(x))};
55 \addplot[color=blue] {1-x^2/2+x^4/24};
56 \end{axis}
57 \end{tikzpicture}
58 \end{tabular} \\ \hline
59 $\sin(x) = \sum\limits_{k=0}^{n}(-1)^k\frac{x^{2k+1}}{(2k+1)!}+o_{x \rightarrow 0}(x^{2n+2}) $ & \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\sin(x)$ & $=$ & $x$ & $-$ & $\frac{x^3}{6}$ & $+$ & $\frac{x^5}{120}$ & $+$ & $o_{x \rightarrow 0}(x^6)$ \\
60 & & \begin{tikzpicture}[scale=0.3, transform shape]
61 \begin{axis}[domain=-2:2,legend pos=outer north east]
62 \addplot[color=red] {sin(deg(x))};
63 \addplot[color=blue] {x};
64 \end{axis}
65 \end{tikzpicture}
66 & & \begin{tikzpicture}[scale=0.3, transform shape]
67 \begin{axis}[domain=-2:2,legend pos=outer north east]
68 \addplot[color=red] {sin(deg(x))};
69 \addplot[color=blue] {x-x^3/6};
70 \end{axis}
71 \end{tikzpicture}
72 & & \begin{tikzpicture}[scale=0.3, transform shape]
73 \begin{axis}[domain=-2:2,legend pos=outer north east]
74 \addplot[color=red] {sin(deg(x))};
75 \addplot[color=blue] {x-x^3/6+x^5/120};
76 \end{axis}
77 \end{tikzpicture}
78 \end{tabular} \\ \hline
79 $e^x = \sum\limits_{k=0}^{n} \frac{x^{k}}{k!}+o_{x \rightarrow 0}(x^{n}) $ & \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $e^x$ & $=$ & $1$ & $+$ & $x$ & $+$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^3}{6}$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\
80 & & \begin{tikzpicture}[scale=0.3, transform shape]
81 \begin{axis}[domain=-2:2,legend pos=outer north east]
82 \addplot[color=red] {e^x};
83 \addplot[color=blue] {1};
84 \end{axis}
85 \end{tikzpicture}
86 & & \begin{tikzpicture}[scale=0.3, transform shape]
87 \begin{axis}[domain=-2:2,legend pos=outer north east]
88 \addplot[color=red] {e^x};
89 \addplot[color=blue] {1+x)};
90 \end{axis}
91 \end{tikzpicture}
92 & & \begin{tikzpicture}[scale=0.3, transform shape]
93 \begin{axis}[domain=-2:2,legend pos=outer north east]
94 \addplot[color=red] {e^x};
95 \addplot[color=blue] {1+x+x^2/2};
96 \end{axis}
97 \end{tikzpicture}
98 & & \begin{tikzpicture}[scale=0.3, transform shape]
99 \begin{axis}[domain=-2:2,legend pos=outer north east]
100 \addplot[color=red] {e^x};
101 \addplot[color=blue] {1+x+x^2/2+x^3/6};
102 \end{axis}
103 \end{tikzpicture}
104 \end{tabular}\\ \hline
105 $ \ln(1+x) = \sum\limits_{k=0}^{n} (-1)^{k+1}\frac{x^{k}}{k}+o_{x \rightarrow 0}(x^{n}) $ & \begin{tabular}{!{\qquad}ccccccccc!{\qquad}} $\ln(1+x)$ & $=$ & $x$ & $-$ & $\frac{x^2}{2}$ & $+$ & $\frac{x^3}{3}$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\
106 & & \begin{tikzpicture}[scale=0.3, transform shape]
107 \begin{axis}[domain=0:2,legend pos=outer north east]
108 \addplot[color=red] {ln(x+1)};
109 \addplot[color=blue] {x};
110 \end{axis}
111 \end{tikzpicture}
112 & & \begin{tikzpicture}[scale=0.3, transform shape]
113 \begin{axis}[domain=0:2,legend pos=outer north east]
114 \addplot[color=red] {ln(x+1)};
115 \addplot[color=blue] {x-x^2/2};
116 \end{axis}
117 \end{tikzpicture}
118 & & \begin{tikzpicture}[scale=0.3, transform shape]
119 \begin{axis}[domain=-1:1,legend pos=outer north east]
120 \addplot[color=red] {ln(x+1)};
121 \addplot[color=blue] {x-x^2/2+x^3/3};
122 \end{axis}
123 \end{tikzpicture}
124 \end{tabular} \\ \hline
125 $ \frac{1}{1+x} = \sum\limits_{k=0}^{n} (-1)^k x^{k}+o_{x \rightarrow 0}(x^{n}) $ & \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $\frac{1}{1+x}$ & $=$ & $1$ & $-$ & $x$ & $+$ & $x^2$ & $-$ & $x^3$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\
126 & & \begin{tikzpicture}[scale=0.3, transform shape]
127 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
128 \addplot[color=red] {1/(1+x)};
129 \addplot[color=blue] {1};
130 \end{axis}
131 \end{tikzpicture}
132 & & \begin{tikzpicture}[scale=0.3, transform shape]
133 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
134 \addplot[color=red] {1/(1+x)};
135 \addplot[color=blue] {1-x)};
136 \end{axis}
137 \end{tikzpicture}
138 & & \begin{tikzpicture}[scale=0.3, transform shape]
139 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
140 \addplot[color=red] {1/(1+x)};
141 \addplot[color=blue] {1-x+x^2};
142 \end{axis}
143 \end{tikzpicture}
144 & & \begin{tikzpicture}[scale=0.3, transform shape]
145 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
146 \addplot[color=red] {1/(1+x)};
147 \addplot[color=blue] {1-x+x^2-x^3};
148 \end{axis}
149 \end{tikzpicture}
150 \end{tabular} \\ \hline
151 $ \frac{1}{1-x} = \sum\limits_{k=0}^{n} x^{k}+o_{x \rightarrow 0}(x^{n}) $ & \begin{tabular}{!{\qquad}ccccccccccc!{\qquad}} $\frac{1}{1-x}$ & $=$ & $1$ & $+$ & $x$ & $+$ & $x^2$ & $+$ & $x^3$ & $+$ & $o_{x \rightarrow 0}(x^3)$ \\
152 & & \begin{tikzpicture}[scale=0.3, transform shape]
153 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
154 \addplot[color=red] {1/(1-x)};
155 \addplot[color=blue] {1};
156 \end{axis}
157 \end{tikzpicture}
158 & & \begin{tikzpicture}[scale=0.3, transform shape]
159 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
160 \addplot[color=red] {1/(1-x)};
161 \addplot[color=blue] {1+x)};
162 \end{axis}
163 \end{tikzpicture}
164 & & \begin{tikzpicture}[scale=0.3, transform shape]
165 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
166 \addplot[color=red] {1/(1-x)};
167 \addplot[color=blue] {1+x+x^2};
168 \end{axis}
169 \end{tikzpicture}
170 & & \begin{tikzpicture}[scale=0.3, transform shape]
171 \begin{axis}[domain=-0.5:0.5,legend pos=outer north east]
172 \addplot[color=red] {1/(1-x)};
173 \addplot[color=blue] {1+x+x^2+x^3};
174 \end{axis}
175 \end{tikzpicture}
176 \end{tabular} \\ \hline
177 \Xhline{2\arrayrulewidth}
178 \end{tabular}
179 }
180\end{table}
181\vfill
182\hspace{0pt}
183\pagebreak
184
185\end{document}