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111年 - 111 國立臺北大學日間學士班轉學生招生考試試題_經濟學系日間學士班二年級：微積分#116873
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2. The area of the region bounded by the curves x=1-y
2
and x=y
2
-1 is__(2)__.
其他申論題
6. If is the Taylor polynomial of order 4 generated by at 0, then the constant in front of x4, c4=__(6)__.
#499433
9. The domain ofis__(9)__.
#499434
10. If f(x)=x+cosx,then=__(10)__.
#499435
II. (50 points) Fill in the following blanks.1. If the integraland c≥0, then the value of c equals __(1)__.
#499436
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
(a) If x2y +y3 = 2 and y(1) = 1. Find y'(1) and yn(1) by implicit differentiation. [10%]
#499441
(b) Find all relative extreme values of f(x) = 2x3 -3x2-12x+4. [10%]
#499442
(a) Evaluate cos2 x sin x dx. [10%]
#499443
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