question 1:

Consider the direction field for the differential equation y' = f(x, y) which is shown below. (The slope of each line segment gives the value of y' at that point.) 2.00 175 150 D 125 100 0.75 0.50 B 0.25 0.00 A 0.0 0.5 10 15 2.0 XAssume that y = 1 at a = 0 (the red dot). (a) Using this direction field to estimate the value of y' at each point (xi, yi), apply Euler's method with stepsize h = 1 to estimate the value of y at ac = 2. Which blue dot corresponds to this estimated value of y ? OA OB OC OD (b) Using only the direction field, which blue dot appears to show the true exact value of y at x = 2? OA OB OC ODThis is a drag-and-drop question. Click on the letters A, B,C,D in the rectangles below to drag them into the correct position. The graph shows four curves. These curves are the graphs of f(a), f'(x), f"(a ) and g(), where there is no relation between g(a ) and f(a) or any of its derivatives. Identify which curve is which. 10 O 0.5 . . . 1.0 2.0 3.0 -5 f (z ) is shown by curve f'(x) is shown by curve D, f"() is shown by curve g(x) is shown by curve A B C