MAT-1120 Final: MATH 1120 App State Spring2009 Final Exam formB
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/12 points) approximations (a) let f (x) = x + 7, a = 4, b = 2, and n = 3. Find the mid-point approximation ofr 2 (don"t worry about simplifying). 4 x + 7 dx (b) same setup as in part (a). Let l = left hand, r = right hand, m = mid-point, and t = trapezoid approximations. In addition let i = r b a f (x) dx. List the approximations and the de nite integral from least to greatest. [example: l r m t i (which would be an incorrect answer. )] (c) express the following limit as a de nite integral and then evaluate the integral: lim n . /8 points) solve the following initial value problem: 2 dy dx. /12 points) integrate (a) z x2 + x + 3 x3 + x dx (b) z x ln|x| dx (c) z cos5(x) dx. /9 points) determine whether each of the following integrals converge or diverge.
