Solution 2.3:10d
From Förberedande kurs i matematik 1
(Difference between revisions)
(Ny sida: {{NAVCONTENT_START}} <center> Bild:2_3_10d.gif </center> {{NAVCONTENT_STOP}}) |
m |
||
(4 intermediate revisions not shown.) | |||
Line 1: | Line 1: | ||
- | { | + | 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>. |
- | + | ||
- | + | ||
+ | {| align="center" | ||
+ | |align="center"|[[Image:2_3_10_d1-1.gif|center]] | ||
+ | |width="10px"| | ||
+ | |align="center"|[[Image:2_3_10_d1-2.gif|center]] | ||
+ | |- | ||
+ | |align="center"|<small>The region ''x''² ≤ ''y''</small> | ||
+ | || | ||
+ | |align="center"|<small>The region ''y'' ≤ ''x''</small> | ||
+ | |} | ||
+ | |||
+ | |||
+ | 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. | ||
+ | |||
+ | |||
+ | {| align="center" | ||
+ | |align="center"|[[Image:2_3_10_d2.gif|center]] | ||
+ | |- | ||
+ | |align="center"|<small>The region ''x''² ≤ y ≤ x</small> | ||
+ | |} |
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 |