Show that the Linear Approximation to (x) x at x 9 yields the estimate 9 h 3 1 6 h Set K 0 01 and show that (x) K for x 9 Then verify numerically that the error E satisfies Eq (5) for h 10 n , for 1 n 4 ( )2 E...

Let fxx Then 9 3 fx x2 and f9 Therefore by the Linear Approximation f9hf ...

Show that the Linear Approximation to (x) = x at x = 9 yields the estimate 9

Question:

Show that the Linear Approximation to ƒ(x) = √x at x = 9 yields the estimate √9 + h − 3 ≈ 1/6 h. Set K = 0.01 and show that |ƒ"(x)| ≤ K for x ≥ 9. Then verify numerically that the error E satisfies Eq. (5) for h = 10⁻ⁿ, for 1 ≤ n ≤ 4.

- (.)2 E