Math1500Fall2022Exam1A

Name: ID #: Math 1500: Exam 1 Instructor: Dustin Belt September 21, 2022 Version A Instructions: • This exam has 9 pages containing 28 problems, which are worth a total of 100 points. Please make sure that all pages are included. • Fill in your name and student ID number on the provided scan tron answer sheet. • Questions 1-6 are True/False Questions while Questions 7-28 are Multiple Choice Questions. Your answers to these questions must be en- tered into the provided Student Answer Sheet . You may also wish to mark your answer on your exam booklet, but only responses cor- rectly recorded on the Student Answer Sheet will be graded. Be sure to indicate your answer on the Student Answer Sheet by completely filling in the appropriate letter. • Indicate the letter of your Discussion Section in the table below. Failing to do this correctly will result in all sorts of ill will wished upon you by the graders and absolves them any responsibility should your exam be lost. • Have your MUID card out and visible on your desk at all times. • You may use a 3” × 5” note card. No other notes, books, calculators, or other resources are allowed. • Turn off and put away your cell phone. • Make sure there are no loose papers or books in your general area. • Read each problem carefully. • You have 60 minutes to complete this exam. Good luck! Questions Points Score 1-28 100 Indicate your Discussion Section: Time Instructor Section 8:00am Noguera Rodriguez A 10:00am Gregory E 10:00am Flores F 11:00am Gregory G 11:00am Flores H 11:00am Lisk J 2:00pm Cairatti K 10:00am Moore M 2:00pm Noguera Rodriguez P 3:00pm Allbritain Q 3:00pm Katz R 1:00pm Moore S 1:00pm Cairatti V 1:00pm Katz W

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Math 1500: Fall 2022 Exam 1 Version A Page 2 of 9 MULTIPLE CHOICE (4 points each) For each of the following questions, indicate the correct answer on the provided Student Answer Sheet. No explanation is necessary. No partial credit will be given. Question 7. (4 points) In exploring the function f ( x ) , the following table of values was obtained: x f ( x ) 2 . 9 1 . 4871 2 . 95 1 . 4936 2 . 99 1 . 4972 2 . 995 1 . 4985 2 . 999 1 . 4993 x f ( x ) 3 . 1 - 1 . 4765 3 . 05 - 1 . 4874 3 . 01 - 1 . 4889 3 . 005 - 1 . 4956 3 . 001 - 1 . 4974 Based on this information, what is the best conclusion that can be made about the lim x → 3 f ( x ) ? A.) lim x → 3 f ( x ) is about 1 . 5 B.) lim x → 3 f ( x ) probably exists, but it is impossible to tell what its value will be from this information. C.) lim x → 3 f ( x ) most likely does not exist. D.) lim x → 3 f ( x ) will mot likely be the same as f (3) E.) lim x → 3 f ( x ) is about 3 Question 8. (4 points) Consider the graph of the function y = f ( x ) given below. What is lim x → 3 f ( x ) ? A.) 0 B.) 1 C.) 2 D.) 3 E.) This limit does not exist.

Math 1500: Fall 2022 Exam 1 Version A Page 3 of 9 Question 9. (4 points) Consider the graph of the function y = f ( x ) given below. What is lim x → 7 + f ( x ) ? A.) 0 B.) 1 C.) 2 . 5 D.) 4 E.) This limit does not exist. For questions 10 to 19, evaluate the given limit. Question 10. (4 points) lim x → 4 x - 2 1 - √ x A.) - 2 B.) - 1 3 C.) 0 D.) 23 E.) This limit does not exist. Question 11. (4 points) lim x → 3 + x - 4 x - 3 A.) 0 B.) 1 C.) 2 D.) ∞ E.) -∞

Math 1500: Fall 2022 Exam 1 Version A Page 5 of 9 Question 15. (4 points) lim x → 1 f ( x ) where 2 x ≤ f ( x ) ≤ x 2 + 1 for all x A.) 2 B.) 1 C.) 0 D.) This limit does not exist. E.) It is impossible to answer this question without more information. Question 16. (4 points) lim x → 4 - | 3 x - 12 | x - 4 A.) This limit does not exist. B.) - 3 C.) - 1 D.) 1 E.) 3 Question 17. (4 points) lim x →-∞ x 4 + x 2 + 9 x 2 + 4 x + 5 A.) 2 B.) 9 5 C.) 0 D.) -∞ E.) ∞ Question 18. (4 points) lim x →∞ 3 x 5 - 7 x 2 + x + 3 9 + 5 x + 6 x 4 + 4 x 5 A.) ∞ B.) 0 C.) 1 3 D.) 1 2 E.) 3 4 Question 19. (4 points) lim x →∞ √ 9 x 6 + x 2 + x + 1 2 x 3 + 2 x + 9 A.) ∞ B.) -∞ C.) 0 D.) 3 2 E.) 9 2

Math 1500: Fall 2022 Exam 1 Version A Page 6 of 9 Question 20. (4 points) Consider the function: f ( x ) =    x 2 - 2 x - 8 x - 4 for x = 4 c for x = 4 What should the value of c be in order for f ( x ) to be continuous at x = 4 . A.) c = 8 B.) c = 6 C.) c = 4 D.) c = 2 E.) c = - 1 Question 21. (4 points) Consider the function f ( x ) = 4 x - x 2 . If f ( x ) is to be computed using the limit definition of the derivative, which of the following limits should be considered? A.) lim h → 0 4 h - h 2 h B.) lim h → 0 4( x + h ) - ( x + h ) 2 - 4 x + x 2 h C.) lim h → 0 4( x + h ) - ( x + h ) 2 - 4 x - x 2 h D.) lim h → 0 4 x - x 2 + h - 4 x + x 2 h E.) lim h → 0 4 x - x 2 + h - 4 x - x 2 h Question 22. (4 points) The following limit represents the derivative of some function f ( x ) at some number x = a . Choose an appropriate pair of f and a below. lim h → 0 √ 9 + h - 3 h A.) f ( x ) = √ x + 9 , a = 3 B.) f ( x ) = √ x + 9 , a = 9 C.) f ( x ) = √ x - 3 , a = 3 D.) f ( x ) = √ x, a = 3 E.) f ( x ) = √ x, a = 9

Math 1500: Fall 2022 Exam 1 Version A Page 8 of 9 Question 25. (4 points) Let B ( y ) = 3 y 5 . What is B ( y ) ? A.) - 15 y 6 B.) 3 5 y 4 C.) - 3 5 y 6 D.) - 15 y 4 E.) - 3 5 y 4 Question 26. (4 points) Find the equation of the tangent line to the curve y = 5 x 2 - 4 x + 3 at the point (1 , 4) A.) y = 6 x - 2 B.) y = 9 x - 5 C.) y = 36 x - 32 D.) y = x + 3 E.) y = 4 x Question 27. (4 points) The equation of motion of a particle is s ( t ) = 1 3 t 3 + 5 2 t 2 - 14 t + 18 , where s is in meters and t is in seconds. Find the acceleration of the particle at the moment when t = 3 . A.) 8 m/s 2 B.) 9 m/s 2 C.) 10 m/s 2 D.) 11 m/s 2 E.) 12 m/s 2

Math 1500: Fall 2022 Exam 1 Version A Page 9 of 9 Question 28. (4 points) Consider the graph of y = f ( x ) given below: Which of the following graphs best represents the graph of y = f ( x ) ? A.) B.) C.) D.)