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(x)| 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? a sample program for f(x) = e x is posted on blackboard course library. (in python)

Assume that two parallel arrays have been declared and initialized: healthoption an array of type char that contains letter codes for different healthcare options and annual cost an array of type int. the i-th element of annual cost indicates the annual cost of the i-th element of healthoption. in addition, there is an char variable, best2.write the code necessary to assign to best2 the health option with the lower annual cost, considering only the first two healthcare options. thus, if the values of healthoption are 'b', 'q', 'w', 'z' and the values of annualcost are 8430, 9400, 7050, 6400 your code would assign 'b' to best2 because 8430 is less than 9400 and is associated with 'b' in the parallel array. (we ignore 'w' and 'z' because we are considering only the first two options.)