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Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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
Transcribed Image Text:Part 2
a) Sketch by hand a slope field for the differential equation y' = x/y. Use it to sketch the four solutions that satisfy the initial
conditions y(0) = 1, y(0) = -1, y(2) = 1, and y(-2) = 1.
Use a grapher to create a slope field for the particular solutions in part (a) and include a screen capture of the slope field.
Verify your solutions in parts (a) and (b) by solving the differential equation explicitly. What type of curve is each solution
b)
c)
curve?
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- Match the differential equation with its direction field. y' = sin(10x) sin(10y) 20) -0.31 1-0.2 \ +0x1 \ \ 0- - 0.2 / /03 -0.3- 0.2 -0.1 0.1 0.2 -0.3 -2 -1 1 -2 -1 1 0.3- Give reasons for your answer. The slopes at each point are independent of y, so the slopes are the same along each line parallel to the y-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 0, and y' > 0 for 0 < x < n/10, 0 < y < n/10. O The slopes at each point are independent of x, so the slopes are the same along each line parallel to the x-axis. Note that for y = 10, y' = 0. o y' = sin(10x) sin(10y) = 0 on the lines x = 0 and y = 10. o y' = sin(10x) sin(10y) = 0 on the line y = -x + 1/10, and y' = -1 on the line y = -x. | |||arrow_forwardNewton’s theory of gravitation states that the weight of a person x feet above sea level is given by:arrow_forwardLet y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $40000 in the account. Each year the account earns 6% interest, and you withdraw $3000. Write the differential equation modeling this situation. dy dt y(0) =arrow_forward
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- Consider the differential equation: dy/dx = y(3 - y) 1) Use the slope field plotter to plot different solutions corresponding to A: (0,-2); B: (0,1); C: (0,3); D: (0,4). You can drag each point to the correct place if they're somewhere else on the plane, or click on the point and redefine. Capture a screenshot showing all the solution curves and insert below. f'(x)=y(3-y) Kin/5 -5 Density Length dy de -8 Step size 0.1 Ymas y (3-9) Input. ✔Solution A Solution B Solution C Solution D DCQ= AC: 2) To what value does y(x) approach, as x → ∞, for the solutions corresponding to B,C, and D? To what value does y(x) approach, as x →∞, for the solution corresponding to A? Why is it different from the others? Be specific and answer in terms of what you know about the slope field and its effect on the solution. - 3) Use wolframalpha.com or something similar to find the particular solution corresponding to each of the points A,B,C,D. How is the solution through Point C different from the other…arrow_forwardAt t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Determine when the tank will overflow and create a differential equation to determine how much salt will be in the tank after 1 hour.arrow_forward
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