11x1 t03 05 regions in the plane (2011)
TRANSCRIPT
Regions In The PlaneTo draw a region, first you have to sketch the curve.
Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
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
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 >)
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.
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
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
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
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
2 2( ) 9ii x y
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
test (0,0)2 20 0 9
0 9
2 2( ) 9ii x y y
x3
32 2 9x y
–3
–3
test (0,0)2 20 0 9
0 9
2( ) 4ii y x
2( ) 4ii y x y
x
2
2–2
24y x
2( ) 4ii y x y
x
2test (0,0)
20 4 00 2
24y x
2–2
2( ) 4ii y x y
x
2
2–2
test (0,0)20 4 0
0 2
24y x
2( ) 4ii y x y
x
2
2–2
test (0,0)20 4 0
0 2
24y x
2( ) and 3 4iv y x y x
2( ) and 3 4iv y x y x y
x
2y x
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1)
2( ) and 3 4iv y x y x y
x
2y x2y x
20 10 1
test (0,1) 3 4y x
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
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
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( ) 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
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)
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*
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)