Übungen Analysis I:Übungszettel 4 – Truth-Quark

Aus Truth-Quark

(Unterschied zwischen Versionen)

Wechseln zu: Navigation, Suche

Aktuelle Version vom 15:22, 8. Mai 2010

Inhaltsverzeichnis

1 Aufgabe 1
- 1.1 a)
2 Aufgabe 2
- 2.1 a)

Aufgabe 1

a)

$LaTeX: p \in \mathbb N$

Please install Java to use this page.

$LaTeX: p \in \mathbb Q$

Please install Java to use this page.

Aufgabe 2

a)

$LaTeX: M_1\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon 0 \le x \right\rbrace$ Graue Fläche
$LaTeX: M_2\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon x \le -y \le -x \right\rbrace$ Rote Fläche
$LaTeX: M_3\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon y = -x \right\rbrace$ Schwarze Gerade
$LaTeX: M_4\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon (x-2)^2 + y^2 = 1^2 \right\rbrace$ Grüner Kreisrand

Please install Java to use this page.

@@ Zeile 1: / Zeile 1: @@
 ==Aufgabe 1==
+===a)===
+<br /><math>p \in \mathbb N</math>
+<ggb_applet width="100%" height="500"  version="3.2" ggbBase64="UEsDBBQACAAIADmKqDwAAAAAAAAAAAAAAAAMAAAAZ2VvZ2VicmEueG1s3Vlbb9s2FH5efwWhhyFGa1vUxbI3q0WaYECBbH1IVgxbloKWaJuLbhWpVG7d/77Di2zZzsXJUiDZi0WR1OE53/nOOSQ9flOnCbqiJWd5Flq4Z1uIZlEes2wWWpWYdofWm9cvxjOaz+ikJGialykRoeX2HEv2V+z1ix/GfJ5/RiRRUz4w+jm0piTh1EK8KCmJ+ZxSsdFPqpoljJSL95N/aCT4ekALeZcVlVh1Rml8wvjqva+WLBImjtkVi2mJkjwKrYEPykPrAy0Fi0gSWp6te5zQcrYGocuVo/O8ZF/yTMjpoqyM8Cn0IMTZFwqYOLJv3FemjmkVJSxmJJPmKD1gEkKfWSzmcq7vgUzKZnPQNhgMtbgoz8v4dMEFTVH9Jy1zUG2AeyPsDUYD3x2O8Ciw0MKM+LjnDj1vMHQc33eCIaAICoMmjmvDSDAcOv4osDHG8M2NQ2phenVKhQBfckRqyo2JaFayuN1+x9/mSbyCu8hZJo5IIapS0cA1XadiIdcC1Epp4GE2S6jpc8BJcxpdTvL6VKPmatFni0J9otSZzI7yJC9RKf3hwwTznOinmiP1XM2y1RxbzTAypNDVOB45aoZ6TvRTzUpYplUzduPGaGw3yzCOZAcIl+xt4EjIhAIVLFRlTJw0L0CZS2Mp1vN/q9IJRE2bNCuR+JFEjvtbbBtf0jKjiaZUBn6t8oqjK8ndVmTENGIpvOoB3OAqvfU7aKC7YzoraaO4jjmNlxq127zd6h73Gy2kEhyUjQQkDzBISGNkbAuIKtmKiZA9MmwSmlKIKaHokFUpLVm0gmZiydVgicos5Ns9o4LKLLlKElt4tiyG8R1iYdsxtIGcUswJtHomKhKygJzRNlSJ/DWPzfKGRDxRySVlTWZMSW10awLeke1aDrujkT+AYA5GAxz4DtB/EVpduzcaQag7XuANR74HcW2hKavpOtjaCahl0prAYg5MySjnKso0gCsWZ+BphT7klsJoyQsq5au2MOGHCjBaBfNqDWCXdop0Tw15mssa0KBLoA7UhXQN6t/pP3Kz/9qu2YzmLbfcrs7UqDM9qDsoRAdgHOoiMuHwfnFAOvAju/qIdK5TeFpliqRr8lh3g3wdA43TjJR17O9jpr0n++x9GGBvYxblaUqyGGUkheFfGoOlJCaLKSK2gpFgoKXiBnE0SbQBlWgmzbVoI/BuLOc3Y+nfhuU+0exjHcy++13g9G+E83bC823Cq0CHDPDIlNk3YeHdhNX11xlLeXvC86QS9DSCvJ+d5JHKG40Xmv2LbZuE5qoGpLCRatycs9YG7RVN2xlL2vg4GeutSREH/BWaH/BOp5Gl9i7XZQUzsPr+P7tO1Z6HElQVWy6xX5FJ4m/3hsPA9m3sDOzAs13YKH5pxa3emMk9qJLl3o3TYYNTF0B6hboPwerwyWDVhqr76FgdtTj1IKCOngxQ3e+L1PEmqx6C1fGTweoR42+zLJ/SmezfqspvdVU+2qnE0e2VmBtpDT7RsyjEa5hxLwg8KDmO72BvCOgawG0DMYzCUdb3Auz6Huyt9y7kcPD9lOk5XB+xWFokLGJiBXEia8u7TMCBi6rtzO456pLSQh5f32dnJcm4vPnQc1rns3v5+Vj7+XDHz/H9/Bz/r/zcfV6O3k19mUl9BL1EP36qcvGz/r0u4wlar/2Y7Sa8DRd91+OF2tFtmmnuvThsdaeNKvoObGA1+DrX3TF4Zm937RYTSQp4WDs92KOUnAFG2GCqkSxCg+gdgOovny2ot+CnLg4kft5++Dkb+J0v6/PlxwL9FKLzhE7FwTmv0o9fWYi/XWRoWX9ky4viXF3qdS6+4n7xLTznn0rxV/H312W9vMheLhcw41uI9/eD8+T8wPgJOaN/3N899p3uwfqspO/a7n0qh51l3dnnZF7c82RePItCcd+T+Q7hZ4bsM305VCg097gEmj0Qns1d6VPDp9++lVV/XJj/bl7/C1BLBwi8lgtzxQUAAO0ZAABQSwECFAAUAAgACAA5iqg8vJYLc8UFAADtGQAADAAAAAAAAAAAAAAAAAAAAAAAZ2VvZ2VicmEueG1sUEsFBgAAAAABAAEAOgAAAP8FAAAAAA==" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />
+----
+<br /><math>p \in \mathbb Q</math>
 <ggb_applet width="100%" height="500" version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />
@@ Zeile 6: / Zeile 16: @@
 <math>M_1\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon 0 \le x \right\rbrace</math> Graue Fläche<br />
 <math>M_2\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon x \le -y \le -x \right\rbrace</math> Rote Fläche<br />
-<math>M_3\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon y = -x \right\rbrace</math>Schwarze Gerade<br />
+<math>M_3\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon y = -x \right\rbrace</math> Schwarze Gerade<br />
-<math>M_4\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon (x-2)^2 + y^2 = 1^2 \right\rbrace</math>Grüner Kreisrand<br />
+<math>M_4\colon=\left\lbrace \mathbb C \ni z=x+ \mathrm i \cdot y \colon (x-2)^2 + y^2 = 1^2 \right\rbrace</math> Grüner Kreisrand<br />
 <ggb_applet width="100%" height="500"  version="3.2" ggbBase64="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" framePossible = "false" showResetIcon = "false" showAnimationButton = "true" enableRightClick = "false" errorDialogsActive = "true" enableLabelDrags = "false" showMenuBar = "false" showToolBar = "false" showToolBarHelp = "false" showAlgebraInput = "false" allowRescaling = "true" />
 [[Kategorie:Übungen_Analysis_I]]