[考古] 一些綜合的考古問題
n 1
(1) lim Σ -------------- =?(Answer ”None” if the limit does not exist. )
n→∞ i=1 √(n^2+ni)
1 x t^2
(1) Find lim ------∫ -------------- dt
x→0 x^3 o t^4 + 1 (變換的話 我該怎麼令？)
(2)Integrate f ( x,y,z ) = x-3y^2+z over the line segment C
joining the points ( 1,1,0 ) to the point ( 1,1,1 ).
(1)Which is not a relative (local) extreme point of the function
f(x,y) = xyz-(x^2 +y^2)/2?
(a) (1,1) (這題得意思是我該怎麼做？)
(b) (1,-1)
(c) (-1,1)
(d) (-1,-1)
(e) (0,0)
(3)The minimum of f(x,y,z) = 4x – 2y – 3z subject to the constraint
2x^2+y^2-3z=0 (這方面的題目都沒有教過，完全自己讀，所以不太熟)
(不知道怎麼下手怎麼做才好？)
(4)Find the Jordan curve C that maximizes the line integral and the
corresponding maximum
8 2 1
Evaluate the integral ∫ ∫ ------------ dydx
0 3 1+y^4
√x
好多觀念若有若無的
好茫然
希望高手多多指點！
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