[心得] 微積分去死吧...
這是符麥克今天考的期末考
1.
proof:
1 p!q!
∫ x^p(1-x)^q dx = ____________ for all non-negative integers p,q
0
(p+q+1)!
2.
f(x) = √(x+1/x)
show漸近線是√x
還有畫f(x)圖形
3.
計算:
x^3 - 2x^2 - 10x + 13
∫ ___________________________ dx
x^4 + 5x^3 + 17x^2 + 13x
4.
It can be proved that a rope hanging a meters above the ground with
both ends fixed at two poles having a distance of 2b meters between
them takes the shape of the curve
x/a -x/a
ae + ae
f(x) = ___________________
2
-b<=x<=b
(a) Compute the length of the rope.
(b) Assume that the rope starts to swing.What is the surface area
of the solid enclosed by the rope.
5.
compute the following limit
0 sin(t)
x∫ _____ dt
x t
lim ________________
x->0
x^3 t^2
∫ e dt
x^2
6.
Determine for which real numbers a the following integral is convergent.
∞ dx
∫ ________________
0
a^2√x + √x^3
Compute the values of the corresponding integrals.
Bouns題
1.
dx
∫ _______________
x^2006 - 2005x
2.
1 2005 2006 2006 2005
∫ ( √1-(x) - √1-(x) ) dx
0
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