Re: [考古] 95成大
※ 引述《dodo1654 (secret)》之銘言：
: 1.Compute the following limit:
: １ ｎ
: (a) lim － Σ √[(3i/n)^7+(3i/n)^4]
: n→∞ ｎ i=1
: X 1
: (b) lim [ (-----)-(-----)].
: n→∞ lnX X-1
: x
: e ln(x+e) 1
: 2.Let f(x)=∫ -------------- dx defined on (-1,∞).
: 1 √(x^4+x^2+5)
: (a) Show that f is a strictly increasing function.
: -1
: (b) Find (f )'(0).
: 1 -2/3
: 3.Compute the improper integral ∫ x lnx dx.
: 0
3x^(1/3)lnx - S 3x^(-2/3)dx
= 0 - 0 - [9] = -9
P.S. lim lnx/x^(-2/3) = lim 1/x * (-3/2) * x^(5/3) = 0
: 1 √(1-x^2 ) 2 2
: 6.Compute the iterated integral ∫∫ sin(x +y )dydx.
: 0 0
Pi/2 1
= S S sin(r^2)rdrdt
0 0
= Pi/4 * (-cos1 + 1)
: １ ８
: 7.Find the local extreme values of the function f(x,y)= xy +－+－ for xy ≠ 0.
: ｘ ｙ
: 8.Use the method of Lagrange Multiplier to find the maximum value of the
: 3
: function f(x,y,z) = x+3y-2z defined on R subject to the constraint
: 2 2 2
: x +y +z =14.
: 以上也煩請版上的高手大大們幫忙解惑一下
: 感謝!
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◆ From: 122.124.99.94
※ 編輯: Honor1984 來自: 122.124.99.94 (07/11 02:37)
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※ 編輯: Honor1984 來自: 122.124.104.61 (07/11 12:38)
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