# Answer to Question #67676 in Python for John

Question #67676

Consider the finite-difference approximation

df/d x ≈ −f (x + 2∆) + 8f (x + ∆) − 8f (x − ∆) + f (x − 2∆)/(12∆)

(1)1. Write a function finite_difference(f, x, Delta) that approximates d f /d x for a given Python

function f, point x, and perturbation Delta using Eq. (1).

2. Compute df/dx |x=1 for f (x ) = cos(x ) using your function and ∆ = 0.4, ∆ = 0.2, and ∆ = 0.1.

3. Compute the corresponding absolute errors (i.e., |y' appx − y' actual |). Name these error_0_4, error_0_2, and error_0_1.

4. Use these errors, and the corresponding ∆’s to estimate the order of this method. Name this order.

df/d x ≈ −f (x + 2∆) + 8f (x + ∆) − 8f (x − ∆) + f (x − 2∆)/(12∆)

(1)1. Write a function finite_difference(f, x, Delta) that approximates d f /d x for a given Python

function f, point x, and perturbation Delta using Eq. (1).

2. Compute df/dx |x=1 for f (x ) = cos(x ) using your function and ∆ = 0.4, ∆ = 0.2, and ∆ = 0.1.

3. Compute the corresponding absolute errors (i.e., |y' appx − y' actual |). Name these error_0_4, error_0_2, and error_0_1.

4. Use these errors, and the corresponding ∆’s to estimate the order of this method. Name this order.

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