Euler's Method (calculation of the second point)
Now that we have calculated the first point on the approximation to Y(t),
we can use the point (t1 , y1 ) and the Y'(t1
) to find the coordinates for the second point (t2 , y2
).
For the purposes of calculation, remember that
Y'(t )= 2t+1 and (t1 , y1 ) = (0.5, 1.5)
Student Questions...
9. Calculate the rate of change, Y'(t1 ).
10. Using your answer from question 9, calculate 
y2?
11. Using y2
calculated in question 10, calculate y2?
12. State the coordinates of this second estimated point.
13. Is the value of y2 an over estimate of Y or an
underestimate of Y at t = 1?