私立中原大學八十八學年度研究所招生考試命題紙

所組別 :企業管理學系乙組
資訊管理學系甲組
會計學系乙組 		科目 :微積分 考試時間 : 05月01日第4節
  1. (40%)Find

  2. (10%)Find the equation of the tangent line to the graph of　y=2x•xx　at the point(1,2).

  3. (10%)if g is differentiable and　　,find g'(3)=?

  4. (10%)Find the volume of the solid generated by revolving about the y-axis, the region bounded by the curve y=x2, the x-axis, and the line x=2.

  5. (10%)The total cost of producing and selling 100x units of a commodity per week is
    C(x)=1000+33x-9x2+x3
    Find
    1. the level of production at which the marginal cost is a minimum, and
    2. the minimum marginal cost.

  6. (20%)
    1. Sketch the region R bounded by y=1-x2, the y-axis, the x-axis and the line x=2.
    2. Find the area of R.
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