Re: [微積] 幾題~~~~麻煩
※ 引述《dreamenjoy (今天也很爽)》之銘言:
: 1.
: 2 √4-y^2 √4-x^2-y^2
: ∫ ∫ ∫ z√x^2+y^2+z^2 dzdxdy
: 0 0 0
: π/2 π/2 2
: = ∫ ∫ ∫ 為何積分範圍改這樣呢???
: 0 0 0
誰知道你的變數改成什麼阿XD
: 2.
: Find dy/dx if x^y-y^x=0
f = x^y-y^x
y-1 y
dy fx y x - x lny
── = - ── = - ────────
dx fy y x-1
x lny - x y
: 3.
: 2 x^3
: ∫---------- dx
: 0 (2+x^2)^3
2
x 2
∫────── dx
2(2 + x^2)^3
x^2 = u
u
= ∫────── du
2 (2 + u )^3
1 1 2
= ── ∫ [─── - ──── ] du
2 (2 + u)^2 (2 + u)^3
│4
1 -1 -2 │
= ── [ - (2 + u) + (2 + u) ]│ 0
2
1 1 1 1 1
= ── [ - (── - ── ) + ── - ── ] = ...
2 6 2 36 4
: 4.
: Analyze and sketch the graph of the function f(x)=x^3(x+5)^2
??
: 5.
: Find equations for the lines tangent to the ellipse 4x^2+y^2=72
: that are perpendicular to the line x+2y+3=0
與 x + 2y + 3 = 0 垂直為 2x - y = C
找出橢圓斜率 m = 2 的點
就得到方程式了
: 6. 1
: ---
: x
: Find the value of a if lim(√1+ax-√1-ax) =e
: x→∞
: 7.
: a>0 Find the length of the path trace out by
: x(θ)=3acosθ+acos3θ
: y(θ)=3asinθ-asin3θ as θ reanges from 0 to 2π.
: 8.
: x^2+y^2=1
: x^2+y^2=5
: ∫∫(x^2+2y)dA
: R
: n -x
: 9.∫x e dx=n! Prove that
上下限?
: 滿多題的
: 麻煩各位了~~快考試沒有解答有點著急
好多QQ...
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完整討論串 (本文為第 2 之 2 篇):
微積
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