1. Write a python function named f, which computes the value of f(x) 1 7 (x-x0)...

   

Transcribed Image Text:

1. Write a python function named f, which computes the value of f(x) 1 7 (x-x0) +7, f'(x) = lim h-0 wherex and y are non-negative real numbers. Make sure that x= 0 and y = 1 are the default values for your function. 2. Recalling that the numerical derivative can be defined as f(x+h)-f(x-h) 2h write a python function named derivative, which compute the derivative of any function. 3. Use the above defined functions f and turev for the following. Assume x = 1/7 and y = 0.5. Use numpy to create a mesh for x in [-2,2] with 41, 401, 4001, 40001 points and compute the derivative of fat x = 0. Analyse the mesh dependence of your numerical derivative by generating a table. Also, compare them with the analytical calculation. (The analytical calculation is expected to be done by hand). 1. Write a python function named f, which computes the value of f(x) 1 7 (x-x0) +7, f'(x) = lim h-0 wherex and y are non-negative real numbers. Make sure that x= 0 and y = 1 are the default values for your function. 2. Recalling that the numerical derivative can be defined as f(x+h)-f(x-h) 2h write a python function named derivative, which compute the derivative of any function. 3. Use the above defined functions f and turev for the following. Assume x = 1/7 and y = 0.5. Use numpy to create a mesh for x in [-2,2] with 41, 401, 4001, 40001 points and compute the derivative of fat x = 0. Analyse the mesh dependence of your numerical derivative by generating a table. Also, compare them with the analytical calculation. (The analytical calculation is expected to be done by hand).