please document the code and write this code in python,

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Within the program you MUST document the following: Loop invariants Highlight (via a comment) the decreasing measure in each iteration which guarantees termination Time complexity of the function. Use appropriate notation in your argu- ments/explanations. You will get 0 for not writing appropriate explanations. You will be asked to explain the same during the demo. Write all your code in a single Python file named assignment_3.py. Other specific instructions: Use the Python math library to get the value of it. Part 1 Question 1 In this assignment we will work with iteration (loops) and write their loop in- variants. We already learnt in class how to calculate the value of sin(x) using the Taylor series expansion. We will apply the same ideas to calculate some more useful functions. Implement the following functions using Taylor's Series expansions to find the value of the function for a given x. 1. et = 1 + x + + + + ... Write a function expn(x, n) where n is the number of terms up to which the series is to be expanded and x is the point at which the function is to be evaluated. Example: As e = 1 and let us suppose the number of terms is 2, the function should behave as >>> expn (0, 2) 1 2 2. cos(x) = 1 - x +*+... Example: As cos({ ) = 0 and let us suppose the number of terms is 3, but as the series converges on large values of n. You should obtain >>> cosine (pi/2, 3) 0.0199689 3. 1x = 1+ x + x2 + x3 +... for x) >> inverse (0.5, 3) 1.75 4. In(1 + x) = x - + Example: >>> natural_log(0.5, 2) 0.375 5. tan-'(x) = X- + - ... Example: >>> tan_inv(1, 3) 0.86666667 Instructions: 1. The functions are to be implemented iteratively (using loops). 2. Loop invariants are to be provided for each function using comments. 3. Provide the time complexity of your functions. 4. Your answer should be correct upto 6 decimal digits 3