Math 1131 Practice Exam 1 Spring 2018

Transcription

1 Universit of Connecticut Department of Mathematics Spring 2018 Name: Signature: Instructor Name: TA Name: Lecture Section: Discussion Section: Read This First! Please read each question carefull. All questions are multiple choice. There is onl one correct choice for each answer. Each question is one point. Indicate our answers on the answer sheet. The answer sheet is the ONLY place that counts as our official answers. (1) When ou re done, hand in both the eam booklet and the answer sheet. (2) You will receive the eam booklet back after the eam is graded. The booklet is not graded, but ou ma circle answers there for our records. Calculators are allowed below the level of TI-89. In particular, the TI-Nspire is not allowed. No books or other references are permitted.

2 1. The distance traveled b a particle in t seconds is given b s(t) = t 2 +3t. What is the particle s average velocit over the interval 1 t 4? (A) 8 (B) 0 (C) 2 (D) 5 (E) 1 2. Evaluate the following limit: 3 lim 1 1. (A) 2 (B) (C) 1 (D) + (E) Page 1 of 8

3 3. Using the table below, what appears to be the value of the limit lim f() f() ? (A) (B) (C) 0 (D) 1000 (E) None of the above. 4. If lim f() = 5 what can be said about lim f()? (A) It must be 5 (B) It must be f(3) (C) It must be f(5) (D) It must be 5 (E) It cannot be determined 5. If g() for all 0, what is lim g()? 0 (A) 0 (B) 1 (C) 2 (D) g(0) (E) Cannot be determined Page 2 of 8

4 6. Evaluate the following limit: lim. 4 4 (A) 0 (B) 8 (C) 8 (D) + (E) 7. If lim f() = 3, lim g() =, and lim h() = 4, evaluate the limit lim 1 (A) 1 (B) 3 (C) 13 (D) 5 (E) 7 ( 2f() g() + h() ). Page 3 of 8

5 8. When showing lim(5 + 1) = 11 b the ε δ definition of limits, which of the following is an 2 acceptable value for δ when ε = 0.01? (A) 0.05 (B) 0.5 (C) 0.1 (D) 0.02 (E) Determine the value of the number k that makes the function f() below continuous: { 1 k if < 1, f() = k + if 1. (A) 0 (B) 1 (C) 3/4 (D) 1/2 (E) 15/17 Page 4 of 8

6 10. Consider the function 1 if 0 < < 1, h() = if > 1. Which of the following are true? I. lim h() eists 1 + II. III. lim h() eists 1 lim h() eists 1 IV. h() is continuous at = 1 (A) I onl (B) I and II onl (C) I, II, and III onl (D) IV onl (E) I, II, III, and IV 11. If the function f() is continuous on the interval [ 1, 3], f( 1) = 1, and f(3) = 11, which numbers below are guaranteed to be values of f() b the Intermediate Value Theorem on the interval ( 1, 3)? I. 3 II. III. 2 3π (A) I onl (B) II onl (C) III onl (D) I and II onl (E) I, II, and III Page 5 of 8

7 12. Evaluate the following limit: lim (A) + (B) (C) 0 (D) 1 (E) The function f() = has which of the following? + 8 (A) no vertical or horizontal asmptotes (B) 1 vertical asmptote and 1 horizontal asmptote (C) 2 vertical asmptotes and 1 horizontal asmptote (D) 1 vertical asmptote and 2 horizontal asmptotes (E) 1 vertical asmptote and no horizontal asmptotes Page 6 of 8

8 14. If f() = 3 10 f(1 + h) f(1), then lim is which of the following? (A) f () (B) f (1) (C) Does not eist (D) 0 (E) None of the above 15. If we want to calculate the derivative f () of f() = using the limit definition of the derivative which of the following limits do we need to evaluate and to what does the limit evaluate? 3( + h) + 4 (3 + 4) (A) lim = 3 3( + h) + 4 (3 + 4) (B) lim = 0 3h + 4 (3 + 4) (C) lim = ( + h) + 4 (3h + 4) (D) lim = 3 (E) None of the above. Page 7 of 8

9 16. Below is the graph of the derivative g () of a function g(). Figure 1: Graph of g (). Which of the following is a possible graph of g()? (A) (B) (C) (D) (E) None of the above. It looks like: Page 8 of 8