MATH-106 Midterm: MATH 106 Bates montgomery106Examv2Solution
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Read directions carefully and show all your work. Partial credit will be assigned based upon the correctness, completeness, and clarity of your answers: evaluate the following integrals. (a) z cos12 x sin3 x dx (b) z x2 sin x dx. 1 (c) z 4x2 7x + 1 (x 1)2(x + 1) dx (d) z. Either compute its value to show it converges, or show it diverges. 3: consider the function f (x) = ln(1 + x). (a) find p3(x), the 3rd order taylor polynomial, of f (x) centered at x = 0. Simplify your answer as much as possible, in other words, fractional coe cients must be in lowest terms. (b) use p3(x) to nd estimates for ln(0. 9) and ln(1. 3). Show your work. (c) use taylor"s theorem to approximate the error of your estimate for ln(0. 9), from part (b), on the interval. Recall that error bounds for estimates using a taylor polynomial pn(x) may be determined using:
