Can you please solve it using any programming code? It can be either Python,Java,etc.

X COS X - sin x f(x) = x - sin x Based on your knowledge of Calculus, make a conjecture as to the actual value of this limit. Is f continuous at 0? Write a loop that computes 20 values that approach the limit. Write a loop that stops once your approximations are within 10-5 of your earlier guess. Are there any dangers inherent to writing this kind of a loop? How many times does the program go through the loop? Can it be made faster? Are there any limitations? Use this tool to run a similar analysis on the behavior of g(x) = x2 sin x near 0. X COS X - sin x f(x) = x - sin x Based on your knowledge of Calculus, make a conjecture as to the actual value of this limit. Is f continuous at 0? Write a loop that computes 20 values that approach the limit. Write a loop that stops once your approximations are within 10-5 of your earlier guess. Are there any dangers inherent to writing this kind of a loop? How many times does the program go through the loop? Can it be made faster? Are there any limitations? Use this tool to run a similar analysis on the behavior of g(x) = x2 sin x near 0