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95年 - 95 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題:微積分#113220
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6. Find the absolute maximum and minimum values of
f(x,y,z) = 2x-2y + z
subject to the constraint x
2
+ y
2
+ z
2
=1.
其他申論題
3. Let f(x) = .Then the interval of convergence of f(x) is________. and the interval OF convergence of f'(x) is________.
#483765
4. Let R be the region inside the ellipsoid where a,b,c> 0, and abovethe plane z = b-y, then the volume of the region R is =______.
#483766
(a)
#483767
(b)
#483768
(a)
#483770
(b) dx. Hint: for a > 0,a ≠ 1.
#483771
(a)
#483772
(b)
#483773
9. Show that
#483774
10 Consider the funetion f(x,y) = ax2 + βy2. Find values for a and β so that (a) (0,0) is a local minimum (b) (0,0) is a local maximum, and (c) (0,0) is a saddle.
#483775