MATH-0042 Study Guide - Midterm Guide: Trapezoidal Rule
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For each problem, you should write down all of your work carefully and legibly to receive full credit. When asked to justify your answer, you should use theorems and/or mathemat- ical reasoning to support your answer, as appropriate. There is a list of formulas and four pages of blank paper at the end of the exam. Let t7(x) be the degree 7 taylor polynomial for a function f (x), centered at a = 2. If f (x) = t7(x) for all x, what is f (9)(3): (3 pts. ) (true or false) simpson"s rule is always more accurate than the trapezoid rule, (3 pts. ) The graph of f (x) = e 1/x is given below. Consider its taylor series centered at a = 2 (but please do not nd it!). Find the taylor series centered at a = 0 for f (x) = x ln(1 + x). Express your answer in terms of sigma/summation notation.
