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Def funcion 2 variables a 0 b 0 y -5 -4 -3 -2 -1 0 1 2 3 4 5 x -5 450 459 466 471 474 475 474 471 466 459 450 -4 459 468 475 480 483 484 483 480 475 468 459 -3 466 475 482 487 490 491 490 487 482 475 466 -2 471 480 487 492 495 496 495 492 487 480 471 -1 474 483 490 495 498 499 498 495 490 483 474 0 475 484 491 496 499 500 499 496 491 484 475 1 474 483 490 495 498 499 498 495 490 483 474 2 471 480 487 492 495 496 495 492 487 480 471 3 466 475 482 487 490 491 490 487 482 475 466 4 459 468 475 480 483 484 483 480 475 468 459 5 450 459 466 471 474 475 474 471 466 459 450 -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 450 459 466 471 474 475 474 471 466 459 450 -4 -5 -4 -3 -2 -1 0 1 2 3 4 5 459 468 475 480 483 484 483 480 475 468 459 -3 -5 -4 -3 -2 -1 0 1 2 3 4 5 466 475 482 487 490 491 490 487 482 475 466 -2 -5 -4 -3 -2 -1 0 1 2 3 4 5 471 480 487 492 495 496 495 492 487 480 471 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 474 483 490 495 498 499 498 495 490 483 474 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 475 484 491 496 499 500 499 496 491 484 475 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 474 483 490 495 498 499 498 495 490 483 474 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 471 480 487 492 495 496 495 492 487 480 471 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 466 475 482 487 490 491 490 487 482 47 5 466 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 459 468 475 480 483 484 483 480 475 468 459 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 450 459 466 471 474 475 474 471 466 459 450 y z x curvas de nivel y y -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x -5.0 0.0 4.8 9.0 12.8 16.0 18.8 21.0 22.8 24.0 24.8 25.0 24.8 24.0 22.8 21.0 18.8 16.0 12.8 9.0 4.8 0.0 x -5.0 0.0 4.8 9.0 12.8 16.0 18.8 21.0 22.8 24.0 24.8 25.0 24.8 24.0 22.8 21.0 18.8 16.0 12.8 9.0 4.8 0.0 -4.5 -4.8 0.0 4.3 8.0 11.3 14.0 16.3 18.0 19.3 20.0 20.3 20.0 19.3 18.0 16.3 14.0 11.3 8.0 4.3 0.0 -4.8 -4.5 -4.8 0.0 4.3 8.0 11.3 14.0 16.3 18.0 19.3 20.0 20.3 20.0 19.3 18.0 16.3 14.0 11.3 8.0 4.3 0.0 -4.8 -4.0 -9.0 -4.3 0.0 3.8 7.0 9.8 12.0 13.8 15.0 15.8 16.0 15.8 15.0 13.8 12.0 9.8 7.0 3.8 0.0 -4.3 -9.0 -4.0 -9.0 -4.3 0.0 3.8 7.0 9.8 12.0 13.8 15.0 15.8 16.0 15.8 15.0 13.8 12.0 9.8 7.0 3.8 0.0 -4.3 -9.0 -3.5 -12.8 -8.0 -3.8 0.0 3.3 6.0 8.3 10.0 11.3 12.0 12.3 12.0 11.3 10.0 8.3 6.0 3.3 0.0 -3.8 -8.0 -12.8 -3.5 -12.8 -8.0 -3.8 0.0 3.3 6.0 8.3 10.0 11.3 12.0 12.3 12.0 11.3 10.0 8.3 6.0 3.3 0.0 -3.8 -8.0 -12.8 -3.0 -16.0 -11.3 -7.0 -3.3 0.0 2.8 5.0 6.8 8.0 8.8 9.0 8.8 8.0 6.8 5.0 2.8 0.0 -3.3 -7.0 -11.3 -16.0 -3.0 -16.0 -11.3 -7.0 -3.3 0.0 2.8 5.0 6.8 8.0 8.8 9.0 8.8 8.0 6.8 5.0 2.8 0.0 -3.3 -7.0 -11.3 -16.0 -2.5 -18.8 -14.0 -9.8 -6.0 -2.8 0.0 2.3 4.0 5.3 6.0 6.3 6.0 5.3 4.0 2.3 0.0 -2.8 -6.0 -9.8 -14.0 -18.8 -2.5 -18.8 -14.0 -9.8 -6.0 -2.8 0.0 2.3 4.0 5.3 6.0 6.3 6.0 5.3 4.0 2.3 0.0 -2.8 -6.0 -9.8 -14.0 -18.8 -2.0 -21.0 -16.3 -12.0 -8.3 -5.0 -2.3 0.0 1.8 3.0 3.8 4.0 3.8 3.0 1.8 0.0 -2.3 -5.0 -8.3 -12.0 -16.3 -21.0 -2.0 -21.0 -16.3 -12.0 -8.3 -5.0 -2.3 0.0 1.8 3.0 3.8 4.0 3.8 3.0 1.8 0.0 -2.3 -5.0 -8.3 -12.0 -16.3 -21.0 -1.5 -22.8 -18.0 -13.8 -10.0 -6.8 -4.0 -1.8 0.0 1.3 2.0 2.3 2.0 1.3 0.0 -1.8 -4.0 -6.8 -10.0 -13.8 -18.0 -22.8 -1.5 -22.8 -18.0 -13.8 -10.0 -6.8 -4.0 -1.8 0.0 1.3 2.0 2.3 2.0 1.3 0.0 -1.8 -4.0 -6.8 -10.0 -13.8 -18.0 -22.8 -1.0 -24.0 -19.3 -15.0 -11.3 -8.0 -5.3 -3.0 -1.3 0.0 0.8 1.0 0.8 0.0 -1.3 -3.0 -5.3 -8.0 -11.3 -15.0 -19.3 -24.0 -1.0 -24.0 -19.3 -15.0 -11.3 -8.0 -5.3 -3.0 -1.3 0.0 0.8 1.0 0.8 0.0 -1.3 -3.0 -5.3 -8.0 -11.3 -15.0 -19.3 -24.0 -0.5 -24.8 -20.0 -15.8 -12.0 -8.8 -6.0 -3.8 -2.0 -0.8 0.0 0.3 0.0 -0.8 -2.0 -3.8 -6.0 -8.8 -12.0 -15.8 -20.0 -24.8 -0.5 -24.8 -20.0 -15.8 -12.0 -8.8 -6.0 -3.8 -2.0 -0.8 0.0 0.3 0.0 -0.8 -2.0 -3.8 -6.0 -8.8 -12.0 -15.8 -20.0 -24.8 0.0 -25.0 -20.3 -16.0 -12.3 -9.0 -6.3 -4.0 -2.3 -1.0 -0.3 0.0 -0.3 -1.0 -2.3 -4.0 -6.3 -9.0 -12.3 -16.0 -20.3 -25.0 0.0 -25.0 -20.3 -16.0 -12.3 -9.0 -6.3 -4.0 -2.3 -1.0 -0.3 0.0 -0.3 -1.0 -2.3 -4.0 -6.3 -9.0 -12.3 -16.0 -20.3 -25.0 0.5 -24.8 -20.0 -15.8 -12.0 -8.8 -6.0 -3.8 -2.0 -0.8 0.0 0.3 0.0 -0.8 -2.0 -3.8 -6.0 -8.8 -12.0 -15.8 -20.0 -24.8 0.5 -24.8 -20.0 -15.8 -12.0 -8.8 -6.0 -3.8 -2.0 -0.8 0.0 0.3 0.0 -0.8 -2.0 -3.8 -6.0 -8.8 -12.0 -15.8 -20.0 -24.8 1.0 -24.0 -19.3 -15.0 -11.3 -8.0 -5.3 -3.0 -1.3 0.0 0.8 1.0 0.8 0.0 -1.3 -3.0 -5.3 -8.0 -11.3 -15.0 -19.3 -24.0 1.0 -24.0 -19.3 -15.0 -11.3 -8.0 -5.3 -3.0 -1.3 0.0 0.8 1.0 0.8 0.0 -1.3 -3.0 -5.3 -8.0 -11.3 -15.0 -19.3 -24.0 1.5 -22.8 -18.0 -13.8 -10.0 -6.8 -4.0 -1.8 0.0 1.3 2.0 2.3 2.0 1.3 0.0 -1.8 -4.0 -6.8 -10.0 -13.8 -18.0 -22.8 1.5 -22.8 -18.0 -13.8 -10.0 -6.8 -4.0 -1.8 0.0 1.3 2.0 2.3 2.0 1.3 0.0 -1.8 -4.0 -6.8 -10.0 -13.8 -18.0 -22.8 2.0 -21.0 -16.3 -12.0 -8.3 -5.0 -2.3 0.0 1.8 3.0 3.8 4.0 3.8 3.0 1.8 0.0 -2.3 -5.0 -8.3 -12.0 -16.3 -21.0 2.0 -21.0 -16.3 -12.0 -8.3 -5.0 -2.3 0.0 1.8 3.0 3.8 4.0 3.8 3.0 1.8 0.0 -2.3 -5.0 -8.3 -12.0 -16.3 -21.0 2.5 -18.8 -14.0 -9.8 -6.0 -2.8 0.0 2.3 4.0 5.3 6.0 6.3 6.0 5.3 4.0 2.3 0.0 -2.8 -6.0 -9.8 -14.0 -18.8 2.5 -18.8 -14.0 -9.8 -6.0 -2.8 0.0 2.3 4.0 5.3 6.0 6.3 6.0 5.3 4.0 2.3 0.0 -2.8 -6.0 -9.8 -14.0 -18.8 3.0 -16.0 -11.3 -7.0 -3.3 0.0 2.8 5.0 6.8 8.0 8.8 9.0 8.8 8.0 6.8 5.0 2.8 0.0 -3.3 -7.0 -11.3 -16.0 3.0 -16.0 -11.3 -7.0 -3.3 0.0 2.8 5.0 6.8 8.0 8.8 9.0 8.8 8.0 6.8 5.0 2.8 0.0 -3.3 -7.0 -11.3 -16.0 3.5 -12.8 -8.0 -3.8 0.0 3.3 6.0 8.3 10.0 11.3 12.0 12.3 12.0 11.3 10.0 8.3 6.0 3.3 0.0 -3.8 -8.0 -12.8 3.5 -12.8 -8.0 -3.8 0.0 3.3 6.0 8.3 10.0 11.3 12.0 12.3 12.0 11.3 10.0 8.3 6.0 3.3 0.0 -3.8 -8.0 -12.8 4.0 -9.0 -4.3 0.0 3.8 7.0 9.8 12.0 13.8 15.0 15.8 16.0 15.8 15.0 13.8 12.0 9.8 7.0 3.8 0.0 -4.3 -9.0 4.0 -9.0 -4.3 0.0 3.8 7.0 9.8 12.0 13.8 15.0 15.8 16.0 15.8 15.0 13.8 12.0 9.8 7.0 3.8 0.0 -4.3 -9.0 4.5 -4.8 0.0 4.3 8.0 11.3 14.0 16.3 18.0 19.3 20.0 20.3 20.0 19.3 18.0 16.3 14.0 11.3 8.0 4.3 0.0 -4.8 4.5 -4.8 0.0 4.3 8.0 11.3 14.0 16.3 18.0 19.3 20.0 20.3 20.0 19.3 18.0 16.3 14.0 11.3 8.0 4.3 0.0 -4.8 5.0 0.0 4.8 9.0 12.8 16.0 18.8 21.0 22.8 24.0 24.8 25.0 24.8 24.0 22.8 21.0 18.8 16.0 12.8 9.0 4.8 0.0 5.0 0.0 4.8 9.0 12.8 16.0 18.8 21.0 22.8 24.0 24.8 25.0 24.8 24.0 22.8 21.0 18.8 16.0 12.8 9.0 4.8 0.0 Si desea ver las curvas de nivel proyectadas al plano inferior Haga click sobre el gráfico con botón derecho mousse Seleccione cambiar tipo de gráfico Elija opcción contorno reticular y y -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x -5.0 50.0 45.3 41.0 37.3 34.0 31.3 29.0 27.3 26.0 25.3 25.0 25.3 26.0 27.3 29.0 31.3 34.0 37.3 41.0 45.3 50.0 x -5.0 50.0 45.3 41.0 37.3 34.0 31.3 29.0 27.3 26.0 25.3 25.0 25.3 26.0 27.3 29.0 31.3 34.0 37.3 41.0 45.3 50.0 -4.5 45.3 40.5 36.3 32.5 29.3 26.5 24.3 22.5 21.3 20.5 20.3 20.5 21.3 22.5 24.3 26.5 29.3 32.5 36.3 40.5 45.3 -4.5 45.3 40.5 36.3 32.5 29.3 26.5 24.3 22.5 21.3 20.5 20.3 20.5 21.3 22.5 24.3 26.5 29.3 32.5 36.3 40.5 45.3 -4.0 41.0 36.3 32.0 28.3 25.0 22.3 20.0 18.3 17.0 16.3 16.0 16.3 17.0 18.3 20.0 22.3 25.0 28.3 32.0 36.3 41.0 -4.0 41.0 36.3 32.0 28.3 25.0 22.3 20.0 18.3 17.0 16.3 16.0 16.3 17.0 18.3 20.0 22.3 25.0 28.3 32.0 36.3 41.0 -3.5 37.3 32.5 28.3 24.5 21.3 18.5 16.3 14.5 13.3 12.5 12.3 12.5 13.3 14.5 16.3 18.5 21.3 24.5 28.3 32.5 37.3 -3.5 37.3 32.5 28.3 24.5 21.3 18.5 16.3 14.5 13.3 12.5 12.3 12.5 13.3 14.5 16.3 18.5 21.3 24.5 28.3 32.5 37.3 -3.0 34.0 29.3 25.0 21.3 18.0 15.3 13.0 11.3 10.0 9.3 9.0 9.3 10.0 11.3 13.0 15.3 18.0 21.3 25.0 29.3 34.0 -3.0 34.0 29.3 25.0 21.3 18.0 15.3 13.0 11.3 10.0 9.3 9.0 9.3 10.0 11.3 13.0 15.3 18.0 21.3 25.0 29.3 34.0 -2.5 31.3 26.5 22.3 18.5 15.3 12.5 10.3 8.5 7.3 6.5 6.3 6.5 7.3 8.5 10.3 12.5 15.3 18.5 22.3 26.5 31.3 -2.5 31.3 26.5 22.3 18.5 15.3 12.5 10.3 8.5 7.3 6.5 6.3 6.5 7.3 8.5 10.3 12.5 15.3 18.5 22.3 26.5 31.3 -2.0 29.0 24.3 20.0 16.3 13.0 10.3 8.0 6.3 5.0 4.34.0 4.3 5.0 6.3 8.0 10.3 13.0 16.3 20.0 24.3 29.0 -2.0 29.0 24.3 20.0 16.3 13.0 10.3 8.0 6.3 5.0 4.3 4.0 4.3 5.0 6.3 8.0 10.3 13.0 16.3 20.0 24.3 29.0 -1.5 27.3 22.5 18.3 14.5 11.3 8.5 6.3 4.5 3.3 2.5 2.3 2.5 3.3 4.5 6.3 8.5 11.3 14.5 18.3 22.5 27.3 -1.5 27.3 22.5 18.3 14.5 11.3 8.5 6.3 4.5 3.3 2.5 2.3 2.5 3.3 4.5 6.3 8.5 11.3 14.5 18.3 22.5 27.3 -1.0 26.0 21.3 17.0 13.3 10.0 7.3 5.0 3.3 2.0 1.3 1.0 1.3 2.0 3.3 5.0 7.3 10.0 13.3 17.0 21.3 26.0 -1.0 26.0 21.3 17.0 13.3 10.0 7.3 5.0 3.3 2.0 1.3 1.0 1.3 2.0 3.3 5.0 7.3 10.0 13.3 17.0 21.3 26.0 -0.5 25.3 20.5 16.3 12.5 9.3 6.5 4.3 2.5 1.3 0.5 0.3 0.5 1.3 2.5 4.3 6.5 9.3 12.5 16.3 20.5 25.3 -0.5 25.3 20.5 16.3 12.5 9.3 6.5 4.3 2.5 1.3 0.5 0.3 0.5 1.3 2.5 4.3 6.5 9.3 12.5 16.3 20.5 25.3 0.0 25.0 20.3 16.0 12.3 9.0 6.3 4.0 2.3 1.0 0.3 0.0 0.3 1.0 2.3 4.0 6.3 9.0 12.3 16.0 20.3 25.0 0.0 25.0 20.3 16.0 12.3 9.0 6.3 4.0 2.3 1.0 0.3 0.0 0.3 1.0 2.3 4.0 6.3 9.0 12.3 16.0 20.3 25.0 0.5 25.3 20.5 16.3 12.5 9.3 6.5 4.3 2.5 1.3 0.5 0.3 0.5 1.3 2.5 4.3 6.5 9.3 12.5 16.3 20.5 25.3 0.5 25.3 20.5 16.3 12.5 9.3 6.5 4.3 2.5 1.3 0.5 0.3 0.5 1.3 2.5 4.3 6.5 9.3 12.5 16.3 20.5 25.3 1.0 26.0 21.3 17.0 13.3 10.0 7.3 5.0 3.3 2.0 1.3 1.0 1.3 2.0 3.3 5.0 7.3 10.0 13.3 17.0 21.3 26.0 1.0 26.0 21.3 17.0 13.3 10.0 7.3 5.0 3.3 2.0 1.3 1.0 1.3 2.0 3.3 5.0 7.3 10.0 13.3 17.0 21.3 26.0 1.5 27.3 22.5 18.3 14.5 11.3 8.5 6.3 4.5 3.3 2.5 2.3 2.5 3.3 4.5 6.3 8.5 11.3 14.5 18.3 22.5 27.3 1.5 27.3 22.5 18.3 14.5 11.3 8.5 6.3 4.5 3.3 2.5 2.3 2.5 3.3 4.5 6.3 8.5 11.3 14.5 18.3 22.5 27.3 2.0 29.0 24.3 20.0 16.3 13.0 10.3 8.0 6.3 5.0 4.3 4.0 4.3 5.0 6.3 8.0 10.3 13.0 16.3 20.0 24.3 29.0 2.0 29.0 24.3 20.0 16.3 13.0 10.3 8.0 6.3 5.0 4.3 4.0 4.3 5.0 6.3 8.0 10.3 13.0 16.3 20.0 24.3 29.0 2.5 31.3 26.5 22.3 18.5 15.3 12.5 10.3 8.5 7.3 6.5 6.3 6.5 7.3 8.5 10.3 12.5 15.3 18.5 22.3 26.5 31.3 2.5 31.3 26.5 22.3 18.5 15.3 12.5 10.3 8.5 7.3 6.5 6.3 6.5 7.3 8.5 10.3 12.5 15.3 18.5 22.3 26.5 31.3 3.0 34.0 29.3 25.0 21.3 18.0 15.3 13.0 11.3 10.0 9.3 9.0 9.3 10.0 11.3 13.0 15.3 18.0 21.3 25.0 29.3 34.0 3.0 34.0 29.3 25.0 21.3 18.0 15.3 13.0 11.3 10.0 9.3 9.0 9.3 10.0 11.3 13.0 15.3 18.0 21.3 25.0 29.3 34.0 3.5 37.3 32.5 28.3 24.5 21.3 18.5 16.3 14.5 13.3 12.5 12.3 12.5 13.3 14.5 16.3 18.5 21.3 24.5 28.3 32.5 37.3 3.5 37.3 32.5 28.3 24.5 21.3 18.5 16.3 14.5 13.3 12.5 12.3 12.5 13.3 14.5 16.3 18.5 21.3 24.5 28.3 32.5 37.3 4.0 41.0 36.3 32.0 28.3 25.0 22.3 20.0 18.3 17.0 16.3 16.0 16.3 17.0 18.3 20.0 22.3 25.0 28.3 32.0 36.3 41.0 4.0 41.0 36.3 32.0 28.3 25.0 22.3 20.0 18.3 17.0 16.3 16.0 16.3 17.0 18.3 20.0 22.3 25.0 28.3 32.0 36.3 41.0 4.5 45.3 40.5 36.3 32.5 29.3 26.5 24.3 22.5 21.3 20.5 20.3 20.5 21.3 22.5 24.3 26.5 29.3 32.5 36.3 40.5 45.3 4.5 45.3 40.5 36.3 32.5 29.3 26.5 24.3 22.5 21.3 20.5 20.3 20.5 21.3 22.5 24.3 26.5 29.3 32.5 36.3 40.5 45.3 5.0 50.0 45.3 41.0 37.3 34.0 31.3 29.0 27.3 26.0 25.3 25.0 25.3 26.0 27.3 29.0 31.3 34.0 37.3 41.0 45.3 50.0 5.0 50.0 45.3 41.0 37.3 34.0 31.3 29.0 27.3 26.0 25.3 25.0 25.3 26.0 27.3 29.0 31.3 34.0 37.3 41.0 45.3 50.0 Usted puede modificarcon giro 3D Haga click sobre el gráfico con botón derecho mousse Seleccione Giro 3D Puede modificar Giro X, GiroY, Perspectiva GiroY=90°, Perspectiva=0,1° Curvas de nivel en el plano GiroY=0°, superficie en 3D y y -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 -5.0 -4.5 -4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 x -5.0 -50.0 -45.3 -41.0 -37.3 -34.0 -31.3 -29.0 -27.3 -26.0 -25.3 -25.0 -25.3 -26.0 -27.3 -29.0 -31.3 -34.0 -37.3 -41.0 -45.3 -50.0 x -5.0 -50.0 -45.3 -41.0 -37.3 -34.0 -31.3 -29.0 -27.3 -26.0 -25.3 -25.0 -25.3 -26.0 -27.3 -29.0 -31.3 -34.0 -37.3 -41.0 -45.3 -50.0 -4.5 -45.3 -40.5 -36.3 -32.5 -29.3 -26.5 -24.3 -22.5 -21.3 -20.5 -20.3 -20.5 -21.3 -22.5 -24.3 -26.5 -29.3 -32.5 -36.3 -40.5 -45.3 -4.5 -45.3 -40.5 -36.3 -32.5 -29.3 -26.5 -24.3 -22.5 -21.3 -20.5 -20.3 -20.5 -21.3 -22.5 -24.3 -26.5 -29.3 -32.5 -36.3 -40.5 -45.3 -4.0 -41.0 -36.3 -32.0 -28.3 -25.0 -22.3 -20.0 -18.3 -17.0 -16.3 -16.0 -16.3 -17.0 -18.3 -20.0 -22.3 -25.0 -28.3 -32.0 -36.3 -41.0 -4.0 -41.0 -36.3 -32.0 -28.3 -25.0 -22.3 -20.0 -18.3 -17.0 -16.3 -16.0 -16.3 -17.0 -18.3 -20.0 -22.3 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-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -25 -20.25 -16 -12.25 -9 -6.25 -4 -2.25 -1 -0.25 0 -0.25 -1 -2.25 -4 -6.25 -9 -12.25 -16 -20.25 -25 0,5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -25.25 -20.5 -16.25 -12.5 -9.25 -6.5 -4.25 -2.5 -1.25 -0.5 -0.25 -0.5 -1.25 -2.5 -4.25 -6.5 -9.25 -12.5 -16.25 -20.5 -25.25 1,0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -26 -21.25 -17 -13.25 -10 -7.25 -5 -3.25 -2 -1.25 -1 -1.25 -2 -3.25 -5 -7.25 -10 -13.25 -17 -21.25 -26 1,5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -27.25 -22.5 -18.25 -14.5 -11.25 -8.5 -6.25 -4.5 -3.25 -2.5 -2.25 -2.5 -3.25 -4.5 -6.25 -8.5 -11.25 -14.5 -18.25 -22.5 -27.25 2,0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -29 -24.25 -20 -16.25 -13 -10.25 -8 -6.25 -5 -4.25 -4 -4.25 -5 -6.25 -8 -10.25 -13 -16.25 -20 -24.25 -29 2,5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -31.25 -26.5 -22.25 -18.5 -15.25 -12.5 -10.25 -8.5 -7.25 -6.5 -6.25 -6.5 -7.25 -8.5 -10.25 -12.5 -15.25 -18.5 -22.25 -26.5 -31.25 3,0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -34 -29.25 -25 -21.25 -18 -15.25 -13 -11.25 -10 -9.25 -9 -9.25 -10 -11.25 -13 -15.25 -18 -21.25 -25 -29.25 -34 3,5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -37.25 -32.5 -28.25 -24.5 -21.25 -18.5 -16.25 -14.5 -13.25 -12.5 -12.25 -12.5 -13.25 -14.5 -16.25 -18.5 -21 .25 -24.5 -28.25 -32.5 -37.25 4,0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -41 -36.25 -32 -28.25 -25 -22.25 -20 -18.25 -17 -16.25 -16 -16.25 -17 -18.25 -20 -22.25 -25 -28.25 -32 -36.25 -41 4,5 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -45.25 -40.5 -36.25 -32.5 -29.25 -26.5 -24.25 -22.5 -21.25 -20.5 -20.25 -20.5 -21.25 -22.5 -24.25 -26.5 -29.25 -32.5 -36.25 -40.5 -45.25 5,0 -5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -50 -45.25 -41 -37.25 -34 -31.25 -29 -27.25 -26 -25.25 -25 -25.25 -26 -27.25 -29 -31.25 -34 -37.25 -41 -45.25 -50 Isocuantas C-D Año Q L K L Q0=100 Q0=120 Q0=140 Q0=160 Q0=180 Q0=200 Q0=220 1899 100 100 100 101.0 20 12,012 24,909 46,146 78,724 126,100 192,196 281,394 1900 101 105 107 106.6 40 1,502 3,114 5,768 9,840 15,762 24,025 35,174 1901 112 110 114 112.1 60 445 923 1,709 2,916 4,670 7,118 10,422 1902 122 117 122 119.4 80 188 389 721 1,230 1,970 3,003 4,397 1903 124 122 131 125.4 100 96 199 369 630 1,009 1,538 2,251 1904 122 121 138 126.3 120 56 115 214 364 584 890 1,303 1905 143 125 149 131.9 140 35 73 135 230 368 560 820 1906 152 134 163 142.1 160 23 49 90 154 246 375 550 1907 151 140 176 149.7 180 16 34 63 108 173 264 386 1908126 123 185 137.6 200 12 25 46 79 126 192 281 1909 155 143 198 156.7 220 9 19 35 59 95 144 211 1910 159 147 208 161.9 240 7 14 27 46 73 111 163 1911 153 148 216 164.3 260 5 11 21 36 57 87 128 1912 177 155 226 172.0 280 4 9 17 29 46 70 103 1913 184 156 236 174.7 300 4 7 14 23 37 57 83 1914 169 152 244 172.8 1915 189 156 266 180.0 1916 225 183 298 208.8 1917 227 198 335 228.1 1918 223 201 366 235.8 1919 218 196 387 234.7 1920 231 194 407 235.8 1921 179 146 417 191.7 1922 240 161 431 208.0 Isocuantas Q0=100 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 12012.254306035205 1501.5317882544 444.89830763093437 187.69147353180034 96.098034448281524 55.612288453866675 35.021149580277608 23.461434191475025 16.477715097441976 12.012254306035235 9.0249844523179572 6.9515360567333442 5.467571372797086 4.3776436975346993 3.5591864610474704 Q0=120 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 24908.61052899461 3113.5763161243226 922.5411307035057 389.19703951554089 199.26888423195658 115.3176413379379 72.619855769663658 48.649629939442633 34.16819002605569 24.90861052899465 18.71420776032652 14.414705167242262 11.337555998632036 9.0774819712079537 7.3803290456280344 Q0=140 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 46146.27614206486 5768.2845177581021 1709.121338594998 721.03556471976424 369.17020913651822 213.6401673243742 134.53724822759449 90.129445589970487 63.300790318333085 46.146276142064941 34.670380272024659 26.705020915546815 21.004222185737291 16.8171560284492 93 13.672970708759957 Q0=160 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 78723.509820032326 9840.4387275040353 2915.6855488900915 1230.0548409380067 629.78807856025776 364.46069361126047 229.51460588930743 153.75685511725075 107.98835366259574 78.72350982003249 59.146138106710971 45.557586701407658 35.832275748762989 28.689325736163418 23.325484391120693 Q0=180 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 126099.84080303519 15762.480100379389 4670.3644741864991 1970.3100125474273 1008.7987264242801 583.79555927331091 367.63801983392233 246.28875156842835 172.97646200690684 126.09984080303546 94.7406767866529 69 72.974444909163992 57.396377243074689 45.95475247924027 37.362915793491922 Q0=200 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 192196.06889656329 24024.5086120704 7118.3729220949499 3003.0635765088055 1537.5685511725044 889.7966152618668 560.33839328444174 375.3829470636004 263.64344155907162 192.19606889656376 144.39975123708732 111.22457690773351 87.481141964753377 70.042299160555189 56.946983376759526 Q0=220 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 281394.26447145833 35174.283058932277 10422.009795239221 4396.7853823665382 2251.1541157716638 1302.7512244048989 820.39144160775106 549.59817 27958175 386.00036278663686 281.39426447145894 211.41567578621959 162.84390305061265 128.08113995059543 102.54893020096885 83.376078361913613 Indiferencia E(U) A= 1 m 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.0 19.0 20.0 s U0=10 ; A=1 U0=10 ; A=5 s 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 0.0 10.000 10.000 0.50 0.88 1.88 2.88 3.88 4.88 5.88 6.88 7.88 8.88 9.88 10.88 11.88 12.88 13.88 14.88 15.88 16.88 17.88 18.88 19.88 0.5 10.125 10.625 1.00 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50 8.50 9.50 10.50 11.50 12.50 13.50 14.50 15.50 16.50 17.50 18.50 19.50 1.0 10.500 12.500 1.50 -0.13 0.88 1.88 2.88 3.88 4.88 5.88 6.88 7.88 8.88 9.88 10.88 11.88 12.88 13.88 14.88 15.88 16.88 17.88 18.88 1.5 11.125 15.625 2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 2.0 12.000 20.000 2.50 -2.13 -1.13 -0.13 0.88 1.88 2.88 3.88 4.88 5.88 6.88 7.88 8.88 9.88 10.88 11.88 12.88 13.88 14.88 15.88 16.88 2.5 13.125 25.625 3.00 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50 8.50 9.50 10.50 11.50 12.50 13.50 14.50 15.50 3.0 14.500 32.500 3.50 -5.13 -4.13 -3.13 -2.13 -1.13 -0.13 0.88 1.88 2.88 3.88 4.88 5.88 6.88 7.88 8.88 9.88 10.88 11.88 12.88 13.88 3.5 16.125 40.625 4.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00 11.00 12.00 4.0 18.000 50.000 4.50 -9.13 -8.13 -7.13 -6.13 -5.13 -4.13 -3.13 -2.13 -1.13 -0.13 0.88 1.88 2.88 3.88 4.88 5.88 6.88 7.88 8.88 9.88 4.5 20.125 60.625 5.00 -11.50 -10.50 -9.50 -8.50 -7.50 -6.50 -5.50 -4.50 -3.50 -2.50 -1.50 -0.50 0.50 1.50 2.50 3.50 4.50 5.50 6.50 7.50 5.0 22.500 72.500 5.50 -14.13 -13.13 -12.13 -11.13 -10.13 -9.13 -8.13 -7.13 -6.13 -5.13 -4.13 -3.13 -2.13 -1.13 -0.13 0.88 1.88 2.88 3.88 4.88 5.5 25.125 85.625 6.00 -17.00 -16.00 -15.00 -14.00 -13.00 -12.00 -11.00 -10.00 -9.00 -8.00 -7.00 -6.00 -5.00 -4.00 -3.00 -2.00 -1.00 0.00 1.00 2.00 6.0 28.000 100.000 6.50 -20.13 -19.13 -18.13 -17.13 -16.13 -15.13 -14.13 -13.13 -12.13 -11.13 -10.13 -9.13 -8.13 -7.13 -6.13 -5.13 -4.13 -3.13 -2.13 -1.13 6.5 31.125 115.625 7.00 -23.50 -22.50 -21.50 -20.50 -19.50 -18.50 -17.50 -16.50 -15.50 -14.50 -13.50 -12.50 -11.50 -10.50 -9.50 -8.50 -7.50 -6.50 -5.50 -4.50 7.0 34.500 132.500 7.50 -27.13 -26.13 -25.13 -24.13 -23.13 -22.13 -21.13 -20.13 -19.13 -18.13 -17.13 -16.13 -15.13 -14.13 -13.13 -12.13 -11.13 -10.13 -9.13 -8.13 7.5 38.125 150.625 8.00 -31.00 -30.00 -29.00 -28.00 -27.00 -26.00 -25.00 -24.00 -23.00 -22.00 -21.00 -20.00 -19.00 -18.00 -17.00 -16.00 -15.00 -14.00 -13.00 -12.00 8.0 42.000 170.000 8.50 -35.13 -34.13 -33.13 -32.13 -31.13 -30.13 -29.13 -28.13 -27.13 -26.13 -25.13 -24.13 -23.13 -22.13 -21.13 -20.13 -19.13 -18.13 -17.13 -16.13 8.5 46.125 190.625 9.00 -39.50 -38.50 -37.50 -36.50 -35.50 -34.50 -33.50 -32.50 -31.50 -30.50 -29.50 -28.50 -27.50 -26.50 -25.50 -24.50 -23.50 -22.50 -21.50 -20.50 9.0 50.500 212.500 9.50 -44.13 -43.13 -42.13 -41.13 -40.13 -39.13 -38.13 -37.13 -36.13 -35.13 -34.13 -33.13 -32.13 -31.13 -30.13 -29.13 -28.13 -27.13 -26.13 -25.13 9.5 55.125 235.625 10.00 -49.00 -48.00 -47.00 -46.00 -45.00 -44.00 -43.00 -42.00 -41.00 -40.00 -39.00 -38.00 -37.00 -36.00 -35.00 -34.00 -33.00 -32.00 -31.00 -30.00 10.0 60.000 260.000 Curvas de Indiferencia U0=10 ; A=1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10 10.125 10.5 11.125 12 13.125 14.5 16.125 18 20.125 22.5 25.125 28 31.125 34.5 38.125 42 46.125 50.5 55.125 60 U0=10 ; A=5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10 10.625 12.5 15.625 20 25.625 32.5 40.625 50 60.625 72.5 85.625 100 115.625 132.5 150.625 170 190.625 21 2.5 235.625 260 sigma mu 1,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 1 0.875 0.5 -0.125 -1 -2.125 -3.5 -5.125 -7 -9.125 -11.5 -14.125 -17 -20.125 -23.5 -27.125 -31 -35.125 -39.5 -44.125 -49 2,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 2 1.875 1.5 0.875 0 -1.125 -2.5 -4.125 -6 -8.125 -10.5 -13.125 -16 -19.125 -22.5 -26.125 -30 -34.125 -38.5 -43.125 -48 3,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 3 2.875 2.5 1.875 1 -0.125 -1.5 -3.125 -5 -7.125 -9.5 -12.125 -15 -18.125 -21.5 -25.125 -29 -33.125 -37.5 -42.125 -47 4,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 4 3.875 3.5 2.875 2 0.875 -0.5 -2.125 -4 -6.125 -8.5 -11.125 -1 4 -17.125 -20.5 -24.125 -28 -32.125 -36.5 -41.125 -46 5,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 5 4.875 4.5 3.875 3 1.875 0.5 -1.125 -3 -5.125 -7.5 -10.125 -13 -16.125 -19.5 -23.125 -27 -31.125 -35.5 -40.125 -45 6,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 6 5.875 5.5 4.875 4 2.875 1.5 -0.125 -2 -4.125 -6.5 -9.125 -12 -15.125 -18.5 -22.125 -26 -30.125 -34.5 -39.125 -44 7,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 7 6.875 6.5 5.875 5 3.875 2.5 0.875 -1 -3.125 -5.5 -8.125 -11 -14.125 -17.5 -21.125 -25 -29.125 -33.5 -38.125 -43 8,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 8 7.875 7.5 6.875 6 4.8753.5 1.875 0 -2.125 -4.5 -7.125 -10 -13.125 -16.5 -20.125 -24 -28.125 -32.5 -37.125 -42 9,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 9 8.875 8.5 7.875 7 5.875 4.5 2.875 1 -1.125 -3.5 -6.125 -9 -12.125 -15.5 -19.125 -23 -2 7.125 -31.5 -36.125 -41 10,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10 9.875 9.5 8.875 8 6.875 5.5 3.875 2 -0.125 -2.5 -5.125 -8 -11.125 -14.5 -18.125 -22 -26.125 -30.5 -35.125 -40 11,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 11 10.875 10.5 9.875 9 7.875 6.5 4.875 3 0.875 -1.5 -4.125 -7 -10.125 -13. 5 -17.125 -21 -25.125 -29.5 -34.125 -39 12,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 12 11.875 11.5 10.875 10 8.875 7.5 5.875 4 1.875 -0.5 -3.125 -6 -9.125 -12.5 -16.125 -20 -24.125 -28.5 -33.125 -38 13,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 13 12.875 12.5 11.875 11 9.875 8.5 6.875 5 2.875 0.5 -2.125 -5 -8.125 -11.5 -15.125 -19 -23.125 -27.5 -32.125 -37 14,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 14 13.875 13.5 12.875 12 10.875 9.5 7.875 6 3.875 1.5 -1.125 -4 -7.125 -10.5 -14.125 -18 -22.125 -26.5 -31.125 -36 15,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 15 14.875 14.5 13.875 13 11.875 10.5 8.875 7 4.875 2.5 -0.125 -3 -6.125 -9.5 -13.125 -17 -21.125 -25.5 -30.125 -35 16,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 16 15.875 15.5 14.875 14 12.875 11.5 9.875 8 5.875 3.5 0.875 -2 -5.125 -8.5 -12.125 -16 -20.125 -24.5 -29.125 -34 17,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 17 16.875 16.5 15.875 15 13.875 12.5 10.875 9 6.875 4.5 1.875 -1 -4.125 -7.5 -11.125 -15 -19.125 -23.5 -28.125 -33 18,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 18 17.875 17.5 16.875 16 14.875 13.5 11.875 10 7.875 5.5 2.875 0 -3.125 -6.5 -10.125 -14 -18.125 -22.5 -27.125 -32 19,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 19 18.875 18.5 17.875 17 15.875 14.5 12.875 11 8.875 6.5 3.875 1 -2.125 -5.5 -9.125 -13 -17.125 -21.5 -26.125 -31 20,0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 20 19.875 19.5 18.875 18 16.875 15.5 13.875 12 9.875 7.5 4.875 2 -1.125 -4.5 -8.125 -12 -16.125 -20.5 -25.125 -30 sigma Utilidad mu planos a 4 b -3 c 0 y -5 -4 -3 -2 -1 0 1 2 3 4 5 x -5 -5 -8 -11 -14 -17 -20 -23 -26 -29 -32 -35 -4 -1 -4 -7 -10 -13 -16 -19 -22 -25 -28 -31 -3 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -2 7 4 1 -2 -5 -8 -11 -14 -17 -20 -23 -1 11 8 5 2 -1 -4 -7 -10 -13 -16 -19 0 15 12 9 6 3 0 -3 -6 -9 -12 -15 1 19 16 13 10 7 4 1 -2 -5 -8 -11 2 23 20 17 14 11 8 5 2 -1 -4 -7 3 27 24 21 18 15 12 9 6 3 0 -3 4 31 28 25 22 19 16 13 10 7 4 1 5 35 32 29 26 23 20 17 14 11 8 5 -5 -5 -4 -3 -2 -1 0 1 2 3 4 5 -5 -8 -11 -14 -17 -20 -23 -26 -29 -32 -35 -4 -5 -4 -3 -2 -1 0 1 2 3 4 5 -1 -4 -7 -10 -13 -16 -19 -22 -25 -28 -31 -3 -5 -4 -3 -2 -1 0 1 2 3 4 5 3 0 -3 -6 -9 -12 -15 -18 -21 -24 -27 -2 -5 -4 -3 -2 -1 0 1 2 3 4 5 7 4 1 -2 -5 -8 -11 -14 -17 -20 -23 -1 -5 -4 -3 -2 -1 0 1 2 3 4 5 11 8 5 2 -1 -4 -7 -10 -13 -16 -19 0 -5 -4 -3 -2 -1 0 1 2 3 4 5 15 12 9 6 3 0 -3 -6 -9 -12 -15 1 -5 -4 -3 -2 -1 0 1 2 3 4 5 19 16 13 10 7 4 1 -2 -5 -8 -11 2 -5 -4 -3 -2 -1 0 1 2 3 4 5 23 20 17 14 11 8 5 2 -1 -4 -7 3 -5 -4 -3 -2 -1 0 1 2 3 4 5 27 24 21 18 15 12 9 6 3 0 -3 4 -5 -4 -3 -2 -1 0 1 2 3 4 5 31 28 25 22 19 16 13 10 7 4 1 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 35 32 29 26 23 20 17 14 11 8 5 y z x
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