4. Find a function f(x) substantially different from fr22 that has no antiderivative (in terms of elementary fimctions). In this problem you will approximate J (x) dx in two different ways. (a) Find the Maclaurin series of f (x) and then integrate it to find the Maclaurin series of f f (x) dx. (b) Use the above to find the 5th order Taylor polynomial for f f(x) dx. (c) Use this Taylor polynomial to find a munexical approximation for the definite inte-gral f (x) dx for t = 1 and another value of t that you choose. (d) Use Simpson’s Rule to find an approximation for g f (x) dx for the same two values of t. (e) For your approximations in (c) and (d), use the relevant error bomuis to compare the size of n needed so that the error in your approximation is less than 0.1.

Individual component: This part of the project is to be done individually. This means your submission should be unique and based on your own research (resources you find yourself). 5. Find an application of parametric or polar coordinates not mentioned in the textbook. Research and describe this application using at least three paragraphs and a diagram. Include at least one source in your write-up. 6. Write a brief description of how each member of your group contributed to this project.

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