For dy/dx equals y minus x, what does the direction field segment at (2, 2) look like?

• Horizontal, slope 0
• Vertical, infinite slope
• Rising with slope 1
• Falling with slope minus 1

dy/dx equals x plus 1, y of 0 is 0. Take one Euler step of size 1. What is y1?

Answer: ______________

You halve the Euler step size and redo the same interval. What happens?

• The error roughly halves, at the cost of twice as many steps
• The error stays exactly the same
• The approximation becomes exact
• The error roughly quarters, with the same step count

For y prime = y minus x, what does the field segment at (2, 2) look like?

• Rising with slope 2
• Flat and horizontal
• Falling with slope minus 2

You halve the Euler step size and redo the same interval. What happens to the error?

• It stays exactly the same
• It doubles
• It shrinks to roughly half

You sketch the solution of y prime = x minus y through (0, 1). How does it leave the point?

• Falling with slope minus 1
• Rising with slope 1
• Leaving flat with slope 0

Why does the Euler walk drift away from the true solution?

• It threads segments at right angles
• It reuses the old slope across the whole step
• It uses steps that are too tiny

Continue the same Euler table with step 1. From (1, 1), what is y2?

Answer: ______________

Kim steps from (0, 0) for y prime = x + 1 with h = 1, but measures the slope at x = 1 and gets y1 = 2. What is wrong?

• Tables must start at x = 1
• The step size must equal the slope
• The slope must be measured at the starting point

A student claims Euler steps follow the exact solution curve, so they never drift.

Circle one:   True   False