世新大學九十三學年度日間部二年級轉學生考試

學系別

考試科目

平面傳播科技學系印製組

微積分

※  不可使用計算機(依世新大學入學考試試場規則，考生僅能使用「+ −%」等功能之簡易計算機型)

※    考生請於答案卷內作答

 

   1. (20 points, 5 points each)

       Compute the following limits.

       (1) limx 3   (2x2-3x+5) (2) lim x 3

       (3) limx 0   x    (4) limx 2  f(x), where f(x)=          x2 + 2,x < 2

                                                                                        2x + 1,x = 2

                                                                                        3x,x > 2

 

    2. (15 points)

        Draw a graph of f(x)=x3-9x+1. Your answer must include all significant features

       of the function, such as local maximum and/or local minimum points, points of

       inflection, interval of increasing and decreasing, concavity, asymptotes (if any),

       etc.

 

    3. (20 points, 10 points each)

(1)   Write down the formal definition of ” A function f is continuous at x = a.”

 

(2)   Let f (x) =       Ax+2,x < 1

                                    ,1and f is continuous for all x R(the set of

                                    3x, x

 

              real numbers). Determine the values of a and b.

 

     4. (25 points, 5 points each)

         Evaluate the following integrals.

         (1)  (2)  (3)

         (4) dt (5)

 

      5. (10 points, 5 points each)

(1)   Prove that

(2)   Compute the derivative of ln(x2tan(3x)).

 

      6.   (10 points)

             Let R be the region bounded by the graphs of y = ,y=0, and x=3.Find the

             volume of the solid by revolving R about the linex=4.