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II. (50 points) Fill in the following blanks.
1. If the integraland c≥0, then the value of c equals (1).

其他申論題

5. Write down the range of a, which makes the series converge. __(5)__

6. If is the Taylor polynomial of order 4 generated by at 0, then the constant in front of x4, c4=__(6)__.

9. The domain ofis__(9)__.

10. If f(x)=x+cosx,then=__(10)__.

2. The area of the region bounded by the curves x=1-y2 and x=y2-1 is__(2)__.

3. The slope of the tangent line at the point (1, 1) on the graph of ex-y =2x2-y2equals__(3)__.

4. The value of equals__(4)__.

5. The function f(x,y)=2x3+6xy2-3y3-150x has four stationary points. Among the four, the two saddle points are__(5)__.

(a) If x2y +y3 = 2 and y(1) = 1. Find y'(1) and yn(1) by implicit differentiation. [10%]

(b) Find all relative extreme values of f(x) = 2x3 -3x2-12x+4. [10%]

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