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研究所、轉學考(插大)-微積分
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85年 - 85 中原大學轉學生考試：微積分#124658
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題組內容
1. (10 point) Evaluate the following limits.
(b)
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#530233
IV. Composition (30%)How would you define "success"? What kind of person would you consider "successful"? Please respond to these questions with a short essay of about 300 words.
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IV. Composition (30%)Use an example to support or refute the argument made in passage 2 of the Reading Comprehension Section.
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(a) (sec x - tan x)
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2. (5 point) Let g(x) = x(x - 1)(x - 2)(x - 3). How many real roots has the equationg'(x) = 0? For each, specify an interval containing that root and no others.
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(a) (7 point) ∫ tan⁻¹ x dx
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(b) (8 point)dy dx
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4. (5) if z = f⁻¹(y) = y5 + y3, what is (f⁻¹)'(2)?
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5. (15) Find all the local maximum values (局部極大值), local minimum values(局部極小值), and saddle points (鞍點), of the following functionf(x, y) = x3 + y3 + 3x² - 3y² - 8.
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6. (10 point) Find where C is the arc of the circle x² + y² = 1 from (1, 0) counterclockwise to ().
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