MATH 129 Midterm: MATH 129 University of Arizona Exam 4B S16
31 Jan 2019
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Exam # 4, sections 10. 1 - 10. 3 & 11. 1 - 11. 6. Time allowed: 60 minutes: find the third-order taylor polynomial of (1 + x) ex about the point x = 0. Compute the taylor polynomial directly from the de nition - do not use the table of known taylor series. Use the result above to calculate the exact value of the sum. [ 5 points : pad e approximants are rational functions used to approximate more complicated functions. In this problem, you will derive the pad e approximate to the exponential function. [ 20 points ] (a) let f (x) = (1 + ax)/(1 + bx), where a and b are constants. [ 10 points : for what value(s) of the constant m will u = emx be a solution to the di erential equation. [ 10 points : find the solution to the initial value problem y .
