Let E(h) = hM/2 + /h. a. For the initial-value problem y' = y + 1, 0

Let E(h) = hM/2 + δ/h.
a. For the initial-value problem
y' = −y + 1, 0 ≤ t ≤ 1, y(0) = 0,
Compute the value of h to minimize E(h). Assume δ = 5 × 10−(n+1) if you will be using n-digit arithmetic in part (c).
b. For the optimal h computed in part (a), use Eq. (5.13) to compute the minimal error obtainable.
c. Compare the actual error obtained using h = 0.1 and h = 0.01 to the minimal error in part (b).
Can you explain the results?