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研究所、轉學考(插大)-微積分
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108年 - 108 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試_A2：微積分#112195
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2. Use the limit definition to show that g'(0) exists butg'
, where
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6. Find the volume of the solid obtained by revolving the region bounded by the curves y = -x2 + 4x and y = x2 about the x-axis. Answer :____________
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7. Evaluate . Answer :__________
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8. Find the sum of the series Answer:_________
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1. An open rectangular box is to be constructed from material that costs $3/ft2 for the bottom and $ 1/ft2 for its sides. Find the dimensions of the box of greatest volume that can be constructed for $36.
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a.(6分)
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b. (6分)
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1.A sector with central angle θ is cut from a circle of radius 2 meters, and the edge of the sector are brought together to form a cone, find the magnitude of θ such that the volume of the cone is a maximum.
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2.Find the balance for $1,000 dollars invested at rate 6% for 20 years by (a) compound 4 times per year； (b) continuous compounding.
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3.Let L be any tangent line to the curve (in the first quadrant) Show that the sum of the x- and y- intercepts of L is c.
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(a)
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, where 
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, where