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Slopefields Review and Euler’s Method

Slopefields Review and Euler’s Method. Which of the following differential equations matches the slope field given?. Which of the following differential equations matches the slope field given?. Which of the following differential equations matches the slope field given?.

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Slopefields Review and Euler’s Method

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  1. Slopefields ReviewandEuler’s Method

  2. Which of the following differential equations matches the slope field given?

  3. Which of the following differential equations matches the slope field given?

  4. Which of the following differential equations matches the slope field given?

  5. Which of the following differential equations matches the slope field given?

  6. Euler’s Method Leonhard Euler (1707-1783) was a Swiss mathematician who made enormous contributions to a wide range of mathematics and physics including analytic geometry, trigonometry, geometry, calculus and number theory. He was arguably the greatest mathematician of the eighteenth century (His closest competitor for that title is Lagrange). …is used to approximate values on the solution graph to a differential equation when you can’t actually find the specific solution to the differential equation using separation of variables.

  7. Let’s start with a differential equation you can solve… Given: Find f(0.8) using Δx = 0.2 and f(0) = 4

  8. f(0) = 4 is our reference point so that is where we start. • Plug the reference point into dy/dx to get the slope of the tangent line at that point. 2. Plug Δx into dx (the run of the slope) dy/dx = slope from #1 3. Solve for dy to get the rise 4. Add dy to the previous y to get the new y . 5. Add dx to the previous x to get the new x . 6. Write the new point. (reference point) 7. Repeat the steps until you can answer the question . 4.112

  9. Using integration, solve the differential equation to find the exact value of y when x = 0.8. Find f(0.8) using Δx = 0.2 and f(0) = 4

  10. Use Euler’s Method with Δx = 0.1 to approximate f(3.4) if the point (3,4) appears on the solution graph and 3.6751 • Using integration, solve the differential equation to find the exact value of y when x = 3.4.

  11. Use Euler’s Method with Δx = 1/3 to approximate y(3) if the point (2,1) appears on the solution graph and 148/27 or 5.481

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