The Taylor series of function f expanded around x = a is def taylor2(f,a): f(n) (a)...

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The Taylor series of function f expanded around x = a is def taylor2(f,a): f(n) (a) (x − a)" f(x) = n! Write a function that returns the 2nd-order Taylor series expansion of an aribtrary function. Your function should take 2 arguments-the mathematical function f and the expansion point a-and return a function that takes 1 argument-the input x. Use the functions df and df2 that you wrote previously. The general structure should be: # your code goes here Use your function to evaluate the following: n=0 ≈ ƒ(a) + ƒ'(a)(x − a) + ƒ" (a) (x − a)² a) sin(0.5) and sin(0.75) using a 2nd-order taylor series of sin(x) expanded around x = 0 b) log(0.8) and log(1.2) using a 2nd-order taylor series of log(x) expanded around x = 1 Sample output your code should generate is: The numerical value of sin (0.5) is 0.500000 The exact value of sin(0.5) is 0.479426 The relative error is 0.04291 The Taylor series of function f expanded around x = a is def taylor2(f,a): f(n) (a) (x − a)" f(x) = n! Write a function that returns the 2nd-order Taylor series expansion of an aribtrary function. Your function should take 2 arguments-the mathematical function f and the expansion point a-and return a function that takes 1 argument-the input x. Use the functions df and df2 that you wrote previously. The general structure should be: # your code goes here Use your function to evaluate the following: n=0 ≈ ƒ(a) + ƒ'(a)(x − a) + ƒ" (a) (x − a)² a) sin(0.5) and sin(0.75) using a 2nd-order taylor series of sin(x) expanded around x = 0 b) log(0.8) and log(1.2) using a 2nd-order taylor series of log(x) expanded around x = 1 Sample output your code should generate is: The numerical value of sin (0.5) is 0.500000 The exact value of sin(0.5) is 0.479426 The relative error is 0.04291

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To create a Python function that returns the 2ndorder Taylor series expansion of an arbitrary functi... View the full answer