Solution 2.3:10c

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

Revision as of 12:47, 21 September 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.

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