Solution 2.3:10d

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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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<center> [[Image:2_3_10d.gif]] </center>
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[[Image:2_3_10_d1.gif|center]]
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{| align="center"
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[[Image:2_3_10_d2.gif|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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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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{| align="center"
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|align="center"|[[Image:2_3_10_d2.gif|center]]
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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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