An ant travels in the plane on a curve satisfying dy

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4. An ant travels in the plane on a curve satisfying dy dx = 4 x 2 + 2 x - 3 4 when measured in inches. If the ant begins at the point (1 , 1) and stops when the x -coordinate reaches 2, what total number of inches does the ant travel? (a) 3 2 (b) 2 (c) 9 4 (d) 3 (e) 7 2 (f) π (g) π 2 2 3
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5. Which of the following functions solves the differential equation y = 4 xy ? 6. Find the coefficient of x 5 in the Maclaurin series for the integral x 1 cos( t 2 ) dt . 4
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7. Suppose that y ( x ) is the solution to the differential equation y = xy with initial conditions y (0) = 1 and y (0) = 0. Which of the following is the closest to y (1 / 2)? [Hint: A series solution gives the required accuracy much more easily than does an Euler-type iteration.]
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