課程名稱︰微積分乙上 課程性質︰ 課程教師︰王藹農 開課學院： 開課系所︰ 考試日期（年月日）︰2018/11/8 考試時限（分鐘）：110 試題 : 1.Find tow lines that are tangent to both y=x^2 and y=-x^2+6x-5 2.xy-1=2x+y^2,d^2(y)/(dx)^2=? 3.Xn+1=Xn(2-11Xn),X1=0.1,lim(n→∞)Xn=? 4.lim(x→-∞)(3x+(9x^2-x)^1/2)=? 5.Find the length of the longest pipe that can be carried level around a right-angle corner at the intersection of two corridors of widths 1 meter and 8 meters. 6.∫1(x^-2)dx=? -1 7.∫dx/(-2x^2+8x+4)^1/2=? 8.f(x)=x^2-3x-4/x-2 Find critical points and increasing and decreasing intervals. Find inflection points and concave up and concave down intervals. Find vertical and horizontal asymptotes, slant asymptotes. Sketch the graph. 9.lim(n→∞)sigma(i=1~i=n)sin(iπ/n)/n=? 10.x>0 (x+1/x)^6-(x^6+1/x^6)-2/(x+1/x)^3+(x^3+1/x^3)≧minimum=? Answer 1.y=4x-4,y=2x-1 2.2xy-4x-2y^2+8/(x-2y)^3 3.1/11 4.1/6 5.5√5 6.not R.I. (∞) 7.1/√2(sin^-1(x/√6)+C 8.略 9.2/π 10.6 -- --

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