Lösung 2.3:10c

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 2.3:10c moved to Solution 2.3:10c: Robot: moved page)
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
+
The expression
-
<center> [[Image:2_3_10c-1(2).gif]] </center>
+
<math>\text{1}\ge x\ge \text{ }y^{\text{2}}</math>
-
{{NAVCONTENT_STOP}}
+
means that we have a region which is defined by the two inequalities
-
{{NAVCONTENT_START}}
+
<math>\text{1}\ge x\text{ }</math>
-
<center> [[Image:2_3_10c-2(2).gif]] </center>
+
and
-
{{NAVCONTENT_STOP}}
+
<math>x\ge \text{ }y^{\text{2}}</math>. The first inequality gives us the region to the left of the line
 +
<math>x=\text{1}</math>. If the other inequality had been instead
 +
<math>y=x^{\text{2}}</math>, we would have a region above the parabola
 +
<math>y=x^{\text{2}}</math>, but in our case
 +
<math>x</math>
 +
and
 +
<math>y</math>
 +
have reversed roles, so the inequality
 +
<math>x\ge \text{ }y^{\text{2}}</math>
 +
defines the same type of parabolic region, but with the
 +
<math>x</math>
 +
- and
 +
<math>y</math>
 +
-axes having changed place.
 +
 
[[Image:2_3_10_c1.gif|center]]
[[Image:2_3_10_c1.gif|center]]
 +
Together, the inequalities define the region that is bordered on the left by the parabola and on the right by the line.
[[Image:2_3_10_c2.gif|center]]
[[Image:2_3_10_c2.gif|center]]

Version vom 12:47, 21. Sep. 2008

The expression \displaystyle \text{1}\ge x\ge \text{ }y^{\text{2}} means that we have a region which is defined by the two inequalities \displaystyle \text{1}\ge x\text{ } and \displaystyle x\ge \text{ }y^{\text{2}}. The first inequality gives us the region to the left of the line \displaystyle x=\text{1}. If the other inequality had been instead \displaystyle y=x^{\text{2}}, we would have a region above the parabola \displaystyle y=x^{\text{2}}, but in our case \displaystyle x and \displaystyle y have reversed roles, so the inequality \displaystyle x\ge \text{ }y^{\text{2}} defines the same type of parabolic region, but with the \displaystyle x - and \displaystyle y -axes having changed place.

Together, the inequalities define the region that is bordered on the left by the parabola and on the right by the line.

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_2.3:10c“