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Unformatted text preview: so there are turning points all along this isocline. or m negative and increasing, the slope becomes greater in absolute terms. Consider fnally m = a / b . Then the isocline is y = ax b a b 1 b = ax b a b 2 with intercept a / b 2 . Then along this isocline the slope oF the directional feld is identical to the slope oF the isocline. Hence, the direction felds look quite diFFerent either side oF this isocline. Above it the solution approaches this isocline asymptotically From above. Hence, the Function f ( x ) takes the shape oF the heavy curve in fgure 2.7. In general we do not know the intercept or the turning point. In this instance we consider the approximate integral curves , which are the continuous lines drawn in fgure 2.7. Such integral curves can take a variety oF shapes....
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- Fall '11