11X1 T03 05 regions in the plane (2011)

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11X1 T03 05 regions in the plane (2011)

  1. 1. Regions In The PlaneTo draw a region, first you have to sketch the curve.
  2. 2. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line
  3. 3. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line
  4. 4. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) Circle the point of intersection if it is NOT included (i.e. one is < or >)
  5. 5. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) 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.
  6. 6. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) 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. (i ) y  x  3
  7. 7. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) 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. (i ) y  x  3 y y  x3 3 –3 x
  8. 8. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) 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. (i ) y  x  3 y y  x3 test (0,0) 03 3 –3 x
  9. 9. Regions In The PlaneTo draw a region, first you have to sketch the curve.1) If < or > use a dotted line2) If  or  use a solid line3) 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. (i ) y  x  3 y y  x3 test (0,0) 03 3 –3 x
  10. 10. (ii ) x 2  y 2  9
  11. 11. (ii ) x 2  y 2  9 y 3 x2  y 2  9 –3 3 x –3
  12. 12. (ii ) x 2  y 2  9 y test (0,0) 3 02  02  9 x2  y 2  9 09 –3 3 x –3
  13. 13. (ii ) x 2  y 2  9 y test (0,0) 3 02  02  9 x2  y 2  9 09 –3 3 x –3
  14. 14. (ii ) y  4  x 2
  15. 15. (ii ) y  4  x 2 y 2 y  4  x2 –2 2 x
  16. 16. (ii ) y  4  x 2 y test (0,0) 0  40 2 2 y  4  x2 02 –2 2 x
  17. 17. (ii ) y  4  x 2 y test (0,0) 0  40 2 2 y  4  x2 02 –2 2 x
  18. 18. (ii ) y  4  x 2 y test (0,0) 0  40 2 2 y  4  x2 02 –2 2 x
  19. 19. (iv) y  x 2 and y  3 x  4
  20. 20. (iv) y  x 2 and y  3 x  4 y y  x2 x
  21. 21. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2test (0,1) 0  12 0 1 x
  22. 22. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2test (0,1) 0  12 0 1 x
  23. 23. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2test (0,1) y  3x  4 0  12 0 1 x
  24. 24. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 0 1 04 x
  25. 25. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 0 1 04 x
  26. 26. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 0 1 04 point of intersection x x 2  3x  4
  27. 27. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 0 1 04 point of intersection x x 2  3x  4 x 2  3x  4  0  x  1 x  4   0 x  1 or x  4
  28. 28. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 (4,16) 0 1 04 (1,1) point of intersection x x 2  3x  4 x 2  3x  4  0  x  1 x  4   0 x  1 or x  4
  29. 29. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 (4,16) 0 1 04 (1,1) point of intersection x x 2  3x  4 x 2  3x  4  0  x  1 x  4   0 x  1 or x  4 Exercise 3F; 3ac, 4d, 5cg, 6cd, 7, 10, 12a, 15a, 19, 20, 21a, 23*
  30. 30. (iv) y  x 2 and y  3 x  4 y y  x2 y  x2 y  3x  4test (0,1) test (0,0) y  3x  4 0  12 0 04 (4,16) 0 1 04 (1,1) point of intersection x x 2  3x  4 x 2  3x  4  0  x  1 x  4   0 x  1 or x  4

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