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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.
(a)
(sec x - tan x)
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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.
#530234
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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(b)
#530237
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.
#530238
(a) (7 point) ∫ tan⁻¹ x dx
#530239
(b) (8 point)dy dx
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4. (5) if z = f⁻¹(y) = y5 + y3, what is (f⁻¹)'(2)?
#530241
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.
#530242
(sec x - tan x)
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(sec x - tan x)