Difference between revisions of "Eindimensionale Eingabe"

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| { (x,y) in RR^2 : 1<=x<=2, -x <= y <= 1+x^2} ||  [[File:example07.png|100px]]  || \( \left\{ (x,y) \in \mathbb{R}^2 : 1 \le x \le 2, -x \le y \le 1+x^2  \right\} \)  
 
| { (x,y) in RR^2 : 1<=x<=2, -x <= y <= 1+x^2} ||  [[File:example07.png|100px]]  || \( \left\{ (x,y) \in \mathbb{R}^2 : 1 \le x \le 2, -x \le y \le 1+x^2  \right\} \)  
 
|-
 
|-
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| { (x,y) in RR^2 : 1<=x<=2, -x <= y <= 1+x^2} ||  [[File:example08.png|100px]]  || \( \left\{ (x,y) \in \mathbb{R}^2 : 1 \le x \le 2, -x \le y \le 1+x^2  \right\} \)   
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| LL = { (1,2,-1,3)^T + t (1,-1,2,-1) : t in RR } ||  [[File:example08.png|100px]]  || \( \mathbb{L} = \big\{ (1,2,-1,3)^T + t \; (1,-1,2,-1) : t \in \mathbb{R} \big\} \)   
 
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|-
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|  LL = { (1,2,-1,3)^T + t (1,-1,2,-1) : t in RR } ||  [[File:example09.png|100px]]  || \( \mathbb{L} = \big\{ (1,2,-1,3)^T + t \; (1,-1,2,-1) : t \in \mathbb{R} \big\} \)   
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|  90^o - 30^o  ||  [[File:example09.png|100px]]  || \( 90^\circ - 30^\circ  \)   
 
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|  90^o - 30^o  ||  [[File:example10.png|100px]] || \( 90^\circ - 30^\circ  \)   
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|  (-oo,-1) uu [2,oo)||  [[File:example10.png|100px]]   || \( ( -\infty, -1) \cup [2,\infty) \)   
 
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|-
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| (-oo,-1) uu [2,oo)||  [[File:example11.png|100px]]   || \( ( -\infty, -1) \cup [2,\infty) \)
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| a != 2 => L = {1/2}||  [[File:example11.png|100px]] || \( a \neq 2 \Rightarrow L = \left\{ \frac{1}{2} \right\} \)  
 
|-
 
|-
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| a != 2 => L = {1/2}||  [[File:example12.png|100px]] || \( a \neq 2 \Rightarrow L = \left\{ \frac{1}{2} \right\} \)  
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| (-2,3) nn (3,4) = {} ||  [[File:example12.png|100px]] || \( (-2,3) \cap (3,4) = \{\} \)  
 
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| (-2,3) nn (3,4) = {} ||  [[File:example13.png|100px]] || \( (-2,3) \cap (3,4) = \{\} \)  
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| g : vec(x) = vec(p) + t vec(a), t in RR ||  [[File:example13.png|100px]] || \( g: \vec{x} = \vec{p} + t \vec{a}, t \in \mathbb{R} \)  
 
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|-
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| g : vec(x) = vec(p) + t vec(a), t in RR ||  [[File:example14.png|100px]] || \( g: \vec{x} = \vec{p} + t \vec{a}, t \in \mathbb{R} \)  
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| 2 x_1  - 4 x_2 + 5 x_3 = -7 ||  [[File:example14.png|100px]] || \( 2 x_1 - 4 x_2 + 5 x_3 = -7 \)  
 
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|-
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| 2 x_1  - 4 x_2 + 5 x_3 = -7 ||  [[File:example15.png|100px]] || \( 2 x_1 - 4 x_2 + 5 x_3 = -7 \)  
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| int 1/(1+x^2) dx = arctan(x) + C, C in RR ||  [[File:example15.png|100px]] || \( \displaystyle \int \frac{1}{1+x^2} \, dx = \arctan(x) + C, C \in \mathbb{R} \)
 
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| int 1/(1+x^2) dx = arctan(x) + C, C in RR ||  [[File:example16.png|100px]] || \( \displaystyle \int \frac{1}{1+x^2} \, dx = \arctan(x) + C, C \in \mathbb{R} \) 
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|  ln |x-1| ||  [[File:example16.png|100px]]  || \(  \ln(| x-1 |) \)  
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|-
 
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|  ln |x-1| ||  [[File:example17.png|100px]]  || \(  \ln(| x-1 |) \)  
 
 
|}
 
|}
  

Revision as of 18:41, 29 October 2022

Allgemeine Hinweise

Mathematische Ausdrücke werden als reiner Ascii-Text, also ohne Sonderzeichen, eingegeben, So liefert etwa pi den griechischen Buchstaben \( \pi \).

Wir verwenden implizite Multiplikation, d.h. ein Leerzeichen zwischen zwei Bezeichnern wirkt als Multiplikation: a*b liefert das gleiche Ergebnis wie a b. Ohne Leerzeichen wird der Ausruck allerdings als eigenständiger; Bezeichner ab betrachtet.

Erkannte Funktionen werden in einem speziellen Font dargestellt:
sin(x) liefert \( \sin(x) \), sinc(x) liefert hingegen \( sinc(x) \).

Bei manchen Aufgaben ist die Lösung die leere Menge. Diese wird durch {} dargestellt.


Beispiele

1D-Eingabe 2D-Eingabe Ergebnis
(a+b)^2 Example01.png \( (a + b)^2 \)
sin(pi/4) Example02.png \( \sin \left( \frac{\pi}{4} \right) \)
a^2 + 2 a b + b^2 Example03.png \( a^2 + 2 a \, b + b^2 \)
1/sqrt(1+x^2) Example04.png \( \frac{1}{\sqrt{1+x^2}} \)
x^3/2 Example05.png \( \frac{x^3}{2} \)
x^(3/2) Example06.png \( x^{\frac{3}{2}} \)
{ (x,y) in RR^2 : 1<=x<=2, -x <= y <= 1+x^2} Example07.png \( \left\{ (x,y) \in \mathbb{R}^2 : 1 \le x \le 2, -x \le y \le 1+x^2 \right\} \)
LL = { (1,2,-1,3)^T + t (1,-1,2,-1) : t in RR } Example08.png \( \mathbb{L} = \big\{ (1,2,-1,3)^T + t \; (1,-1,2,-1) : t \in \mathbb{R} \big\} \)
90^o - 30^o Example09.png \( 90^\circ - 30^\circ \)
(-oo,-1) uu [2,oo) Example10.png \( ( -\infty, -1) \cup [2,\infty) \)
a != 2 => L = {1/2} Example11.png \( a \neq 2 \Rightarrow L = \left\{ \frac{1}{2} \right\} \)
(-2,3) nn (3,4) = {} Example12.png \( (-2,3) \cap (3,4) = \{\} \)
g : vec(x) = vec(p) + t vec(a), t in RR Example13.png \( g: \vec{x} = \vec{p} + t \vec{a}, t \in \mathbb{R} \)
2 x_1 - 4 x_2 + 5 x_3 = -7 Example14.png \( 2 x_1 - 4 x_2 + 5 x_3 = -7 \)
int 1/(1+x^2) dx = arctan(x) + C, C in RR Example15.png \( \displaystyle \int \frac{1}{1+x^2} \, dx = \arctan(x) + C, C \in \mathbb{R} \)
x-1| Example16.png \( \ln(| x-1 |) \)

Bezeichner und Operatoren

\( \alpha \): alpha \( \beta \): beta \( \gamma \): gamma \( \delta \): delta \( \epsilon \): epsilon \( \zeta \): zeta
\( \eta \): eta \( \vartheta \): theta \( \iota \): iota \( \kappa \): kappa \( \lambda \): lambda \( \mu \): mu
\( \nu \): nu \( \xi \): xi \( \pi \): pi \( \varrho \): rho \( \sigma \): sigma \( \tau \): tau
\( \varphi \): phi \( \chi \): chi \( \psi \): psi \( \omega \): omega \( \Omega \): Omega
\( \infty \): oo \( \in \): in \( ^\circ \): ^o \( ^\top \): ^T \( \cup \): uu \( \cap \): nn
\( \mathbb{N} \): NN \( \mathbb{Z} \): ZZ \( \mathbb{Q} \): QQ \( \mathbb{R} \): RR \( \mathbb{C} \): CC \( \mathbb{L} \): LL
\( \le \): <= \( \ge \): >= \( \neq \): != \( \Rightarrow \): => \( \Leftrightarrow \): <=>


Funktionen

           arccos, arccosh, arcsin, arcsinh, arctan, arctanh, cos, cosh, cot, det, exp,
           ln, log, sin, sinh, sqrt, tan, tanh, abs, min, max, vec
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