Re: [問題] 微積分(誰會解?) 急~!
※ 引述《corncorn (迴旋夢)》之銘言：
: 1. Find the area of largest rectangle that can be inscribed in a semicircle
: of radius r.
answer:Max area=r^2
: 2. Evaluate the integral
: 1 1 ________
: a) ∫ ∫ √x^3 + 1 dxdy
: 0 √y
1 x^2_______
hint:原式=∫ ∫√x^3 + 1 dydx
0 0
answer:2/9
: 0
: b) ∫ xe^x dx
: -∞
answer:-1
: tanx － x
: 3. Find lim ─────
: x→0 x^3
hint:use L'Hopital's rule
answer:1/3
: 4. Find the equations of the tangent plane and the normal line to the surface
: sin(xyz) ＝ x+2y+3z at the point (2,-1,0)
hint:use the Gradient Vector,so the normal vector=(1/√30,2/√30,5/√30)
answer:the tangent plane => x+2y+5z=0,the normal line => x-2=(y+1)/2=z/5
: 5. Find the radius of convergence and interval of convergence of series
: ∞ (-3)^n · x^n
: Σ ───────
: n＝0 √(n+1)
hint:use Ratio Test
answer:1/3
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