Difference between revisions of "Beispiele 1D- vs. 2D-Eingabe"
(Tabelle Beispiele (1D und 2D) aus Seite "Eindimensionale Eingabe" verschoben)
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Beispiele
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{| class="wikitable" style="margin:auto"
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! 1D-Eingabe !! 2D-Eingabe || Ergebnis
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|-
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| (a+b)^2 || [[File:example01.png|100px]] || \( (a + b)^2 \)
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|-
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| sin(pi/4)  || [[File:example02.png|100px]] || \( \sin \left( \frac{\pi}{4} \right) \)
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|-
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|  a^2 + 2 a b + b^2  || [[File:example03.png|150px]]  || \( a^2 + 2 a \, b + b^2 \)
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|-
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| 1/sqrt(1+x^2)  || [[File:example04.png|100px]] || \( \frac{1}{\sqrt{1+x^2}} \) 
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|-
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| x^3/2 ||  [[File:example05.png|50px]] || \( \frac{x^3}{2} \)
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|-
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| x^(3/2)||  [[File:example06.png|80px]]  || \( x^{\frac{3}{2}} \)
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|-
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| { (x,y) in RR^2 : 1<=x<=2, -x <= y <= 1+x^2} ||  [[File:example07.png|350px]]  || \( \left\{ (x,y) \in \mathbb{R}^2 : 1 \le x \le 2, -x \le y \le 1+x^2  \right\} \)
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|-
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|  LL = { (1,2,-1,3)^T + t (1,-1,2,-1) : t in RR } ||  [[File:example08.png|350px]]  ||  \( \mathbb{L} = \big\{ (1,2,-1,3)^T + t \; (1,-1,2,-1) : t \in \mathbb{R} \big\} \) 
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|-
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|  ||  [[File:example17.png|350px]]  || 
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|-
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|  90^o - 30^o  ||  [[File:example09.png|100px]]  || \( 90^\circ - 30^\circ  \) 
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|  (-oo,-1) uu [2,oo)||  [[File:example10.png|200px]]  || \( ( -\infty, -1) \cup [2,\infty) \) 
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|-
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| a != 2 => L = {1/2}||  [[File:example11.png|200px]]  || \( a \neq 2 \Rightarrow L = \left\{ \frac{1}{2} \right\} \)
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|-
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| (-2,3) nn (3,4) = {} ||  [[File:example12.png|200px]] || \( (-2,3) \cap (3,4) = \{\} \)
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| g : vec(x) = vec(p) + t vec(a), t in RR ||  [[File:example13.png|250px]] || \( g: \vec{x} = \vec{p} + t \vec{a}, t \in \mathbb{R} \)
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|-
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| 2 x_1  - 4 x_2 + 5 x_3 = -7 ||  [[File:example14.png|200px]]  || \(  2 x_1 - 4 x_2 + 5 x_3 = -7 \)
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|-
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| int 1/(1+x^2) dx = arctan(x) + C, C in RR ||  [[File:example15.png|350px]] || \( \displaystyle \int \frac{1}{1+x^2} \, dx = \arctan(x) + C, C \in \mathbb{R} \) 
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|-
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|  ln|x-1| ||  [[File:example16.png|100px]]  || \(  \ln(| x-1 |) \)
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|}

Revision as of 16:46, 18 January 2023

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 \( \mathbb{L} = \big\{ (1,2,-1,3)^T + t \; (1,-1,2,-1) : t \in \mathbb{R} \big\} \)
Example17.png
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 \( \ln(| x-1 |) \)
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