The Linear Approximation to (x) tan x at x 4 yields the estimate tan 4 h 1 2h Set K 6 2 and show, using a plot, that (x) K for x 4, 4 0 1 Then verify numerically that the error E satisfies Eq (5) for h 10 n , for 1 n 4 1 (x) E 2 VI...

Let fx tan x Then f4 1 fx sec x and f4 2 Therefore by the Linear Approximation sh7tanh1 2h f ...

The Linear Approximation to (x) = tan x at x = /4 yields the estimate tan /4

Question:

The Linear Approximation to ƒ(x) = tan x at x = π/4 yields the estimate tan π/4 + h − 1 ≈ 2h. Set K = 6.2 and show, using a plot, that |ƒ"(x)| ≤ K for x ∈ [π/4, π/4 + 0.1]. Then verify numerically that the error E satisfies Eq. (5) for h = 10⁻ⁿ, for 1 ≤ n ≤ 4.

1 - (x)? E 2 VI