C++ Programming help experts: In each prior phase of the project, you analyzed a

Question

C++ Programming help experts:

In each prior phase of the project, you analyzed a different function. We'll change our function to a new function again here, but this time we'll use one that has many practical applications: the standard normal distribution.

Here is the function for the standard normal distribution:

Of course, integrating this by hand is very difficult, and we'll see how our numerical techniques fare with it. If you are not familiar with the shape of the graph of this function, use a graphing calculator or some other utility to view the graph. (You may want to sketch it for your own reference.)

Change your f(x) function to this function. Find its derivative analytically and adjust your derivative function accordingly.

Task 2: Error Analysis of the Derivative

We define the absolute error of an approximation technique at a point x as the absolute value of the difference in the approximation at x and the actual value being approximated at x. In other words, if we were computing the absolute error of the derivative of f(x), we would simply subtract the actual derivative at x from an approximate derivative at x.

Create a function that computes the absolute error in an approximation of the derivative of f(x). It should have the following parameters: the point where we're taking the derivative of f and the approximated value of the derivative (arguments to this parameter will be the outputs of the backward, forward, or center difference functions). This function should use the input approximation and the function you created for f'(x) to find the absolute value of the error in the approximation.

Then create a method that takes in an x-coordinate x0 and an h value anddisplays a report containing the following:

Test drive this function on your own before proceeding, but don't turn in your test driver. Determine which of the approximations you think is best and write about it in your discussion, including concrete data.

Task 3: User Interface

Finally, build a main program that is a user interface to all of these functions and which analyzes the standard normal curve function. Have the program run continuously until the user chooses to quit.

Then give the user the following analysis options:

Explanation / Answer

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