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本文编辑于2019年12月20日

AP, Advanced Placement。是加拿大和美国优秀高中生必备的学习课程。对多数加拿大和美国名牌大学，已经成为入学（尤其是申请热点专业和/或奖学金）的基本要求。

本文所涉及的知识点，不在国内高中教学阶段范围。本系列文章，仅作为中学师生和家长的参考材料。也可作为对部分有兴趣了解北美高中教学（数学）、国内外大学一年级高等数学教学的参考材料。

极限-练习

1. is?

  1. -1
  2. 1
  3. 0
  4. ∞
  5. None of above

2. is?

  1. -1
  2. 1
  3. 0
  4. ∞
  5. None of above

3. is?

  1. ∞
  2. 1
  3. nonexistent
  4. -1
  5. none of these

4. is?

  1. 0
  2. nonexistent
  3. 1
  4. -1
  5. none of these

5. If , and if f is continuous at x = 0, then k =

  1. -1
  2. -½
  3. 0
  4. ½
  5. 1

6. Suppose , then f(x) is continuous

  1. except at x = 1
  2. except at x = 2
  3. except at x = 1 or 2
  4. except at x = 0, 1 or 2
  5. at each real number

7. The graph of , then f(x) has

  1. a horizontal asymptote at y = +½ but no vertical asymptote
  2. no horizontal asymptote but two vertical asymptotes, at x = 0 and x = 1
  3. a horizontal asymptote at y = ½ and two vertical asymptotes, at x = 0 and x = 1
  4. a horizontal asymptote at x = 2 but no vertical asymptote
  5. a hotizontal asymptote at y = ½ and two vertical asymptote, at x = ±1

8. If [x] is the greatest integer not greater than x, then is

  1. ½
  2. 1
  3. nonexistent
  4. 0
  5. non of above

9. If [x] is the greatest integer not greater than x, then is

  1. -3
  2. -2
  3. -1
  4. 0
  5. none of above

Question 10 ~ 14 are based on fig. 1.

Fig.1 Question 10 ~ 14

10. is

  1. = 0
  2. = 1
  3. = 2
  4. does not exist
  5. none of above

11. The function f is defined on [-1, 3]

  1. if x ≠ 0
  2. if x ≠ 1
  3. if x ≠ 2
  4. if x ≠ 3
  5. at each x in [-1, 3]

12. The function f has a removable discontinuity at

  1. x = 0
  2. x = 1
  3. x = 2
  4. x = 3
  5. none of above

13. On which of the following intervals is f continuous?

  1. -1 ≤ x ≤ 0
  2. 0 < x < 1
  3. 1 ≤ x ≤ 2
  4. 2 ≤ x ≤ 3
  5. none of above

14. The function f has a jump discontinuity at

  1. x = -1
  2. x = 1
  3. x = 2
  4. x = 3
  5. none of above

15. is?

  1. -∞
  2. √3 - π/2
  3. √3 + π/2
  4. +∞
  5. none of above

16. is?

  1. 0
  2. 1/12
  3. 1/2
  4. 1/3
  5. not exists

参考答案

1、C； 2、D； 3、C； 4、B； 5、B； 6、B；

7、C； 8、D； 9、E； 10、A； 11、E； 12、C；

13、B； 14、B； 15、E； 16、E。

注：本文参考参考《AP Calculus -- by David Bock, M.S.》。本网站推荐大家使用原版教材。网上信息仅限于个人学习使用，请勿用于任何商业用途。