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103年 - 103 國立中山大學轉學生招生考試試題_應數系二年級：微積分#116874
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題組內容
1.
(a) If x
2
y +y
3
= 2 and y(1) = 1. Find y'(1) and y
n
(1) by implicit differentiation. [10%]
其他申論題
2. The area of the region bounded by the curves x=1-y2 and x=y2-1 is__(2)__.
#499437
3. The slope of the tangent line at the point (1, 1) on the graph of ex-y =2x2-y2equals__(3)__.
#499438
4. The value of equals__(4)__.
#499439
5. The function f(x,y)=2x3+6xy2-3y3-150x has four stationary points. Among the four, the two saddle points are__(5)__.
#499440
(b) Find all relative extreme values of f(x) = 2x3 -3x2-12x+4. [10%]
#499442
(a) Evaluate cos2 x sin x dx. [10%]
#499443
(b) Evaluate dx. [10%]
#499444
(a) Find the interval of convergence of . [10%]
#499445
(b) Find the sum in (a) for x inside the interval of convergence. [10%]
#499446
(a) Find the shortest distance from the point (2,0, 1) to the plane x+y+z=1.[10%]
#499447
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