Solution 2.3:10d

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We can rewrite the double inequality as and . These two inequalities define the region above the parabola and the region below the line .
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We can rewrite the double inequality <math>x^2\le y\le x</math> as <math>x^2\le y</math> and <math>y\le x\,</math>. These two inequalities define the region above the parabola <math>y=x^2</math> and the region below the line <math>y=x</math>.
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[[Image:2_3_10_d1.gif|center]]
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{| align="center"
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|align="center"|[[Image:2_3_10_d1-1.gif|center]]
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|width="10px"|&nbsp;
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|align="center"|[[Image:2_3_10_d1-2.gif|center]]
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|align="center"|<small>The region ''x''²&nbsp;≤&nbsp;''y''</small>
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|align="center"|<small>The region ''y''&nbsp;≤&nbsp;''x''</small>
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|}
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The region which the inequalities both define is the region in the first quadrant that is bordered below by the parabola and above by the line.
The region which the inequalities both define is the region in the first quadrant that is bordered below by the parabola and above by the line.
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[[Image:2_3_10_d2.gif|center]]
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{| align="center"
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|align="center"|[[Image:2_3_10_d2.gif|center]]
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|-
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|align="center"|<small>The region ''x''²&nbsp;≤&nbsp;y&nbsp;≤&nbsp;x</small>
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Current revision

We can rewrite the double inequality \displaystyle x^2\le y\le x as \displaystyle x^2\le y and \displaystyle y\le x\,. These two inequalities define the region above the parabola \displaystyle y=x^2 and the region below the line \displaystyle y=x.


 
The region x² ≤ y The region y ≤ x


The region which the inequalities both define is the region in the first quadrant that is bordered below by the parabola and above by the line.


The region x² ≤ y ≤ x
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