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