MATH15062022PRACTICEFINALEXAM

Consider the following traffic flow diagram, and use it to answer questions 1, 2, 3, 4, and 5. 1. In the augmented matrix of the system of linear equations that describes this traffic flow diagram, what is the line that represents the flow of traffic through intersection D? A) (1 − 1 | 300) B) (1 1 | 300) C) (1 0 0 0 1 0 0 0 | 300) D) ((1 0 0 0 − 1 0 0 0 | 300)) E) None of the above. 2. What is the maximum number of cars that can pass along x 6 ? A) 150 B) 250 C) 300 D) 50 E) None of the above. 3. Suppose we know that at least 170 cars per minute enter the intersection B from the north. Determine the minimum number of cars that will be leaving the intersection E towards south. A) 10 B) 20 C) 30 D) 40 E) None of the above. Copyright 2022 A. McEachern 1

4. Would the system of linear equations describing the traffic flow diagram be square, overdetermined, underdetermined, or none of the above? A) Square B) Overdetermined C) Underdetermined D) None of the above 5. How many free variables are in this system? A) 0 B) 1 C) 2 D) 3 E) None of the above. 6. Consider the following system of linear equations: 2 x + 2 y + 3 z = − 8 x − y + z = 0 What is the solution to this system? A) ( − 2 − 5 4 t, − 2 − 1 4 t, t ) , −∞ < t < ∞ B) (2 − 5 4 t, 2 − 5 4 t, t ) , −∞ < t < ∞ C) (2 − 5 4 t, − 2 − 5 4 t, t ) , −∞ < t < ∞ D) ( − 2 − 5 4 t, 2 − 5 4 t, t ) , −∞ < t < ∞ E) None of the above. 7. The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4720 mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6300 mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese? A) Hot dog = 1060, Cottage cheese = 800 B) Hot dog = -860, Cottage cheese = -1000 C) Hot dog = 1000, Cottage cheese = 860 D) Hot dog = 860, Cottage cheese = 1000 E) None of the above. Copyright 2022 A. McEachern 2

Consider the following function p ( x ) and use it to answer questions 8, 9, 10, 11, 12, 13 and 14. p ( x ) =                  − x 2 − 1 if x < 0 x if 0 < x < π 2 x − sin( x ) if π 2 < x < 3 e x − e 3 + 3 − sin(3) if x ≥ 3 8. At what point is p ( x ) continuous? A) 0 B) Continuous everywhere C) π 2 D) 3 E) All of the above. 9. What kind of discontinuity does p ( x ) have at x = 0? A) A removable discontinuity B) A jump discontinuity C) An infinite discontinuity D) p ( x ) is continuous at this point E) None of the above. 10. What kind of discontinuity does p ( x ) have at x = π 2 ? A) A removable discontinuity B) A jump discontinuity C) An infinite discontinuity D) p ( x ) is continuous at this point E) None of the above. 11. What kind of discontinuity does p ( x ) have at x = 3? A) A removable discontinuity B) A jump discontinuity C) An infinite discontinuity D) p ( x ) is continuous at this point E) None of the above. Copyright 2022 A. McEachern 3

12. What is the lim x → 0 − p ( x )? A) 0 B) π 2 C) -1 D) 3 − sin(3) E) None of the above. 13. What is the lim x → 3 + p ( x )? A) 0 B) π 2 C) -1 D) 3 − sin(3) E) None of the above. 14. What is the lim x →∞ p ( x )? A) e 3 B) π 2 − 1 C) ∞ D) 3 − sin(3) E) None of the above. Copyright 2022 A. McEachern 4

Consider the following picture and use it to answer questions 15 and 16. Let the red graph be f ( x ) and the blue graph be g ( x ). 15. If h ( x ) = f ( x ) g ( x ), what is h ′ (3)? A) -15 B) -9 C) -6 D) 12 E) None of the above. 16. If h ( x ) = f ( x ) − g ( x ), what is h ′ (0)? A) -15 B) -9 C) -6 D) 15 E) None of the above. Copyright 2022 A. McEachern 5