Euler Method

The given slope field is

y(0)=1

Task 1

Go to Tools --> More --> Others. Then use the pen to sketch the graph of y at the particular solution (0,1) Make your graph color blue.

Task 2

Fine the equation of the tangent line at y(0)=1

Task 3

Graph the equation (Algebra --> Write your equation). If your line is not tangent to your sketch then go back and edit your sketch. Use linearization to approximate y(2) . Do you think your answer is accurate ? Why not ?

Task 4

Go to your line and make the interval [0,0.5] Steps: 1) Delete your first graph of the tangent line 2) Paste this command in "Algebra": if(0<x<0.5, mx+b) 3) Put your equation instead of mx+b 4) Increase the thickness to make your graph more visible

Tak 5

Find the equation of the line at x=0.5 using your previous equation and the differential equation above? Then graph it over the interval [0.5,1] using the same steps in Task 4. What do you notice about the two lines you graphed?

Task 6

Find the equation of the tangent line at x=1 ? Then graph it over the interval [1,1.5] Again, what do you notice?

Task 7

Find the equation of the tangent line at x=1.5 ? Then graph it over the interval [1.5,2] Again, what do you notice?

Task 8

Now find y(2) using the equation you found in Task 7, Do you think this value for y(2) is a better approximation than your original approximation in Task 3? Why or Why not?

Task 9

We just used the Euler Method. After completing this activity, what do you think it does?