Numerical Analysis I:

Please show work and try to write neatly so that I may understand (if necessary).

Also please state which programming language you used to write the program, I would prefer it if you used python or Matlab though, but any programming language may be used.

4. Write a computer program that evaluates Pn(x) where Pn(x) is the Taylor series expansion derived in problem (3) above. Verify that \f(x) - Pn (2) satisfies the appropriate error bound. You must be able to convince me by plotting results and checking the error for your approximation that everything was programmed correctly. From your graphs, you will see that the error depends on x. Which values of x would you predict tend to give smaller/larger errors? Does your graph corroborate your intuition? 4. Write a computer program that evaluates Pn(x) where Pn(x) is the Taylor series expansion derived in problem (3) above. Verify that \f(x) - Pn (2) satisfies the appropriate error bound. You must be able to convince me by plotting results and checking the error for your approximation that everything was programmed correctly. From your graphs, you will see that the error depends on x. Which values of x would you predict tend to give smaller/larger errors? Does your graph corroborate your intuition