课程名称︰微积分乙 课程性质︰系必带 课程教师︰王振男 开课学院：医学院 开课系所︰医学系 考试日期（年月日）︰11/11 考试时限（分钟）：150min 试题 : 1.Find the following limits: x x-∫cos(t^2)dt 0 (a)(5%) lim ────────── x→0 6sin^(-1)x-6x-x^2 1 (b)(10%) lim sin(──)((㏑x)^4)*√(x) x→+∞ x 2.(15%)Use the first derivative test to determine all local maxima and minima of f(x) = x^3 - |x| on (-∞,∞) 3.(20%)Evaluate the following limit. 1 n k lim ── Σ cos^(4)(──) n→∞ n k=1 n 4.(15%)Let D be the region under the curve y = √(x) from 0 to 1. Assume that the density function of D is ρ(y) = y. Find the center of mass of D. 5.(10%)Find the equations for the tangent and normal to the cissoid of Diocles y^2(2-x) = x^3 at (1,1) 6.(10%)Find the length of the curve ╭ ｜x = ㏑(sect + tant) - sint ｜ ｜y = cost, 0<=t<=π/3 ╰ 7.(15%) Paper folding： A rectangular sheet of 8.5-in.-by-11-in. paper is placed on a flat surface. One of the corners is placed on the opposite longer edge, as shown in the figure, and held there as the paper is smoothed flat. The problem is to make the length of the crease as small as possible. Call the length L. Try it with paper. D C ┌──── ｜ ︳ R｜\＼ ︳ ｜ \ ＼ ︳ √(L^2-x^2)｜ L\ ＼︳Q (originally at A) ｜ \ /︳ ｜ \/x︳ ￣￣￣￣ B A P a.Show that L^2 = 2x^3/(2x-8.5) b.What value of x minimizes L^2? c.What is the minimum value of L? --

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