Proj-calc - Numerical Calculus Project Part III/Complete Project This project will be all about numerical calculus As you know by now this project

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Numerical Calculus Project Part III/Complete Project This project will be all about numerical calculus. As you know by now, this project is split into three parts. You should already have completed the following: Part I: Numerical Differentiation Functions Part II: Numerical Integration Functions The final part of the project will use the functions from the first two parts and bring them together with an interface and analysis. Your Tasks Task 0: Parts 1 and 2 Begin by making sure your solutions to Parts 1 and 2 of the project are complete and correct, as they are the foundation to this part of the project. Create a new project and copy all of the functions from Part 1 and then all of the functions from Part 2. (Eliminate your test driver main functions.) As before, your functions must be in the order listed in these directions. Do not use prototypes. Task 1: Function to Analyze 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.
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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
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Proj-calc - Numerical Calculus Project Part III/Complete Project This project will be all about numerical calculus As you know by now this project

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