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Unformatted text preview: 高雄㊩㈻大㈻㈨㈩㆒㈻年度㈻士後㊩㈻系招生考試試題 科目:微積分 考試時間: 80 分鐘 共 2 頁第 1 頁 說明:㆒.選擇題用 2B 鉛筆在「答案卡」㆖作答,修正時應以橡皮擦拭,切勿使 用修正液(帶),未遵照正確作答方法而致無法判讀者,考生㉂行負責。 ㆓.試題應隨同試卷繳回,不得攜出試場。 壹、 是非題 20% (是,請在答案卡(A)欄位劃記; 非,請在答案卡(B)欄位劃記。每題 2 分,答錯不倒扣) 3. A function f has an extremum at a number c when f ( c ) 0 . 11 3 2 x 4 dx 8 If f has a local minimum at ( a, b) and f is differentiable at ( a, b ) , then f ( a, b ) 0 . 4. Suppose that lim f ( 1 ) L , n N , then lim f ( x ) L . n 5. Let f ( x ) 6. There exist x [0,1] such that e 7. 8. Let f be a two variables real function. If f is differentiable at ( x0 , y 0 ) , then f is continuous at ( x0 , y 0 ) . If f and g are continuous functions in [a, b], and g(x)0 in [a, b], then there exists a number c in [a, b] such that 1. 2. n x 0 sin x 1 x b a 1 t2 0 e dt . b f ( x) g ( x)dx f (c) g ( x)dx 。 a 9. x x0 . Define F ( x) f (t ) dt . Then F is differentiable for all x in R. 0 x0 x If series a (a and n n 1 n ) are convergent, then n 1 | a n | is also convergent. n 1 10. An integrable function is always continuous. 貳、 選擇題 80% (單選題,每題答對得 5 分,答錯倒扣 1.25 分,未作答者,不給分亦不扣分) x2 11. If x sin (x) f (t )dt , where f is a continuous function , then f ( 4) 0 (A) 2 (B) 1 2 (C) 4 (D) 1 4 (E) 2 x x a 12. For what value of a is it true that lim e. x x a e 1 1 2 (A) a (B) a (C) a (D) a 2 (E) a 2 2 2 e 2 2 13. The area of the region S { ( x , y ) : x 0 , y 1 , x y 4 y } is (A) 2 3 3 2 (B) 2 1 3 32 (C) 4 3 3 (D) 2 3 3 2 (E) 4 3 3 2 1 14. The average value of the function f ( x) cos(t 2 )dt on the interval [0,1] is x (A) sin 1 15. 3 3 0 9 x 2 sin 1 (B) 2 x 2 y 2 dydx cos 1 (C) 4 (A) 3 (D) (B) 6 4 (E) (C) 9 (A) 11 (B) 3 (D) 12 (E) 18 z z 3x 2 3 y , 3 x y , and f ( 0,0 ) 2 , x y 5 3 (C) (D) (E) 1 2 2 16. Suppose that z f ( x , y ) is differentiable such that then f (1, 2) = sin 1 2 【背面㈲試題】 共 2頁 n1 x n 17. Consider the power series (A) ( , ) n . The interval of convergence is (C) ( 1,1] (B) [1,1] 第2頁 (D) [ 1,1) (E) (-1,1) (1h ) e x 2 dx 1 e x 2 dx 0 18. Evaluate the limit. lim 0 = h h 0 (D) 2e (E) Does not exist. (A) 1 (B) 2 (C) e 3 x1 dx = 19. 1 x3 x 2 (A) 1 ln 6 12 (B) 1 ln 3 12 (C) 1 ln 6 12 (D) 1 ln 2 12 2 2 2 2 3 x sin 1 x 0 x 20. Let f ( x ) . Which of the following is incorrect? x0 0 2 (E) 1 ln 2 12 2 3 (A) Function f is continuous at x=0. (B) Function f is differentiable at x=0. (C) Graph of f has a horizontal asymptote y=1. (D) Function f is continuous at x 0 . 6 (E) Function f is concave down for x . 21. Let f ( x, y ) x xy y x y . The absolute maximum of f on rectangle 2 2 R ( x, y ) | 0 x 1,1 y 0 is (A) (B) 1 3 1 4 2 (C) 0 (D) 1 (E) 2 22. The maximum directional derivative of f ( x, y ) x xy 5 y at point (1,1) is 2 (A) 5 (B) 10 (C) 15 (D) 20 (E) 25 2 f ( x) 23. If f is a continuous function in [0, 2], then dx = 0 f ( x) f ( 2 x) 1 3 (A) 0 (B) (C) 1 (D) (E) 2 2 2 2 24. The Fibonacci sequence {fn} was defined by f1 =1, f2 =1, fn=fn-1+fn-2 for n3. Then f n2 1 n 1 f n1 5 10 (E) 2 3 25. The volume of the solids obtained by rotating the region bounded by the curves y = x and y = x2 2 8 3 about the line y = 2 is (A) (B) (C) (D) (E) 2 15 6 15 2 26. D(sec-1 x )= (A) 0 (A) (B) 1 1 x x 1 2 (C) 2 (B) (D) 1 2x x 1 (C) sec 1 x tan 1 2x x (D) sec x tan x 2x (E) tan x 2x = ...
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This note was uploaded on 04/04/2010 for the course SFSEFSEF 489484 taught by Professor Fesfesf during the Winter '08 term at A.T. Still University.

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