MATH 320 Midterm: 2004 Math 320 - Spring Exam 1 Sample
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M arton bal azs: above a certain velocity, the acceleration of vehicles pulled by electric motors (streetcars, trains, trolleybuses, electric cars) can be approximated to be proportional to the inverse of the square of their speed. Assume hence, by neglecting friction and air resistance, that an elevated train traveling with speed v has acceleration in the meter-second system. dv dt. 90 mi/h). (b) (15 points) show that its speed tends to in nity as t . In other words, neglecting friction and air resistance, an electric vehicle accelerates to arbitrary large speeds, just it takes a long way, as seen in question (a). 1: (30 points) solve the initial value problem dy dx. = sin y cos y (a) (15 points) sketch, roughly, a direction eld and classify the critical points. (b) (10 points) determine, from your sketch, the asymptotic behavior of the solution for y(0) = 3x1 + x2 + 2x3 = 4 x2 x3 = 4.
