11 x1 t03 05 regions in the plane (2013)
-
Upload
nigel-simmons -
Category
Education
-
view
419 -
download
0
Transcript of 11 x1 t03 05 regions in the plane (2013)
![Page 1: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/1.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.
![Page 2: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/2.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
![Page 3: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/3.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
![Page 4: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/4.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
![Page 5: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/5.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.
![Page 6: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/6.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.e.g. ( ) 3i y x
![Page 7: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/7.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.e.g. ( ) 3i y x
y
x
3
–3
3y x
![Page 8: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/8.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.e.g. ( ) 3i y x
y
x
3
–3
3y x test (0,0)
0 3
![Page 9: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/9.jpg)
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
2) If or use a solid line
3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
To calculate the region, test a point NOT on the curve.e.g. ( ) 3i y x
y
x
3
–3
3y x test (0,0)
0 3
![Page 10: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/10.jpg)
2 2( ) 9ii x y
![Page 11: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/11.jpg)
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
![Page 12: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/12.jpg)
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
test (0,0)2 20 0 9
0 9
![Page 13: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/13.jpg)
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
test (0,0)2 20 0 9
0 9
![Page 14: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/14.jpg)
2( ) 4ii y x
![Page 15: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/15.jpg)
2( ) 4ii y x y
x
2
2–2
24y x
![Page 16: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/16.jpg)
2( ) 4ii y x y
x
2test (0,0)
20 4 00 2
24y x
2–2
![Page 17: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/17.jpg)
2( ) 4ii y x y
x
2
2–2
test (0,0)20 4 0
0 2
24y x
![Page 18: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/18.jpg)
2( ) 4ii y x y
x
2
2–2
test (0,0)20 4 0
0 2
24y x
![Page 19: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/19.jpg)
2( ) and 3 4iv y x y x
![Page 20: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/20.jpg)
2( ) and 3 4iv y x y x y
x
2y x
![Page 21: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/21.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1)
![Page 22: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/22.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1)
![Page 23: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/23.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x
![Page 24: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/24.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
![Page 25: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/25.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
![Page 26: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/26.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
point of intersection2 3 4x x
![Page 27: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/27.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
point of intersection2 3 4x x
2 3 4 01 4 0
x xx x
1 or 4x x
![Page 28: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/28.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
point of intersection2 3 4x x
2 3 4 01 4 0
x xx x
1 or 4x x
( 1,1)
(4,16)
![Page 29: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/29.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
point of intersection2 3 4x x
2 3 4 01 4 0
x xx x
1 or 4x x
( 1,1)
(4,16)
Exercise 3F; 3ac, 4d, 5cg, 6cd, 7, 10, 12a, 15a, 19, 20, 21a, 23*
![Page 30: 11 x1 t03 05 regions in the plane (2013)](https://reader034.fdocuments.us/reader034/viewer/2022052623/559ef9a31a28abe9768b4778/html5/thumbnails/30.jpg)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x 3 4y x
test (0,0)0 0 40 4
point of intersection2 3 4x x
2 3 4 01 4 0
x xx x
1 or 4x x
( 1,1)
(4,16)