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Ch6-1WS - condition y = 0 when x = 0 5 For Further...

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Mrs. Waldron BC Calculus An Introduction to Slope Fields and Differential Equations 1. For each differential equation below: i. Graph the slope field at the points indicated on the grids. ii. Suppose you know that the point (1, 2) is on the graph of f(x) = y. Sketch a solution curve to the differential equation given this new information. iii. Use what you know of antiderivatives to find an equation for y. Does your slope field accurately portray y? a. dy dx = x 2 b. dy dx = 1 x 2 4 2 -2 -4 4 2 -2 -4 c. dy dx = - 2 x + 2 d. dy dx = 1 - 3 x 2 4 2 -2 -4 4 2 -2 -4
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2. Sketch the solution curve given the slope field below and the initial condition (-2, 1). 3. Sketch the slope field for the differential equations below at the points indicated on the grids. Use the calculator program to confirm your answers. a. dy dx = 1 x 2 + 1 b. dy dx = y 4 2 -2 -4 4 2 -2 -4 5 -5
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c. dy dx = 1 + x 4 d. dy dx = y - x 4 2 -2 -4 4 2 -2 -4 j 4. Go back and use your slope fields in question 2 to sketch the solution curve for the initial
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Unformatted text preview: condition y = 0 when x = 0. 5. For Further Exploration: Use your calculator to plot the slope fields for the equations below: y ' = -x y y ' = -x 2 y y ' = xy 2 + x 2 y ' = y-2 x-1 6. Let f be the function that satisfies the initial value problem 2 dy = y + x dx and f(0) = 1. Use Euler’s method and increments of ∆ x = 0.2 to approximate f(1). Use Euler’s method with increments of ∆ x = 0.2 to approximate the value for the solution of the given initial-value problem: 7. Find f(1) if dy = 2x + y dx and y = 0 when x = 0. (x,y) 2 dy = y + x dx ∆ x dy y = x dx Δ Δ (x+ ∆ x, y+ ∆ y) (x,y) dy = 2x + y dx ∆ x dy y = x dx Δ Δ (x+ ∆ x, y+ ∆ y)...
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