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研究所、轉學考(插大)-微積分
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106年 - 106 台灣綜合大學系統學士班轉學生聯合招生試題：微積分A#98983
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4. (10 points) Evaluate the following integral:
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2. (10 points) If the function is continuous at x= 0, then (a,b) =?
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3. (10 points) Write down the first three terms (three lowest order terms) of the Taylor series of at O. (Hint:)
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5. (10 points) From the equation Solvein terms of x and y
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6. (10 points) Find all values of a so that the series is divergent.
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7. (10 points) Compute the following improper integral
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8. (10 points) Compute the line integralwhereand C is the closed loop formed by traveling from (-2,0) to (4,0) to (3,3) to (-1,3) and back to (-2,0) by straight lines.
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9. (10 points) Given the function F :At (0,0,0), find the direction along which the function decreases most rapidly and find the corresponding rate of change.
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10. (10 points) A rectangular box is formed by cutting four equal corners from a square of side 3 and then folding up (see the figure below). Find the maximum possible volume of the box.
#413807
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