MA121A1_Test1_white_Fall2023

MA121A1 Test1 Fall 2023 Student Name ____________________________ Student BU ID _____________________________ Academic Conduct: If you have never read the CAS Academic Conduct Code, you should do so! I am available for assistance, should you need any. • This is a closed book and closed notes exam. • Calculators and other electronic devices are NOT allowed. • Sharing exam related information/collaboration with others is NOT allowed. • Anyone violating the above mentioned will be reported to the Dean’s Office without fail. Penalties for violating the Academic Conduct Code may include suspension or expulsion from the University. Please sign your name below to acknowledge that you have read and understood the information above. Signature ___________________________________________ Please do not write below this line. ___________________________________________________________________________________ Problem Points Possible Points Earned 1 16 2 8 3 6 4 8 5 22 6 18 7 22

MA121A1 Test1 Fall 2023 Q1 . (16 points) Multiple Choice. Use the graph of ࠵?(࠵?) function provided below to answer to the following multiple-choice questions. Q1.1 Select one correct answer. A. lim !→#$ ࠵?(࠵?) = ࠵?. ࠵?. ࠵? ; ࠵?(−8) = ࠵?. ࠵?. ; ࠵?(࠵?) is discontinuous at ࠵? = −8 B. lim !→#$ ! ࠵?(࠵?) = 2; lim !→#$ " ࠵?(࠵?) = 2; lim !→#$ ࠵?(࠵?) = ࠵?. ࠵?. ࠵? ; ࠵?(−8) = ࠵?. ࠵?. C. lim !→#$ ࠵?(࠵?) = 2 ; ࠵?(−8) = ࠵?. ࠵?. ; ࠵?(࠵?) is discontinuous at ࠵? = −8 D. lim !→#$ ࠵?(࠵?) = ࠵?. ࠵?. ࠵? ; ࠵?(−8) = 2. ; ࠵?(࠵?) is discontinuous at ࠵? = −8 Q1.2 Select one correct answer. A. lim !→#% " ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. , ࠵?(−3) = ࠵?. ࠵?. , ࠵?(࠵?) is discontinuous at ࠵? = −3 B. lim !→#% ! ࠵?(࠵?) = − ∞ ; Vertical asymptote at ࠵? = −3 C. lim !→#% ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. ; Vertical asymptote at ࠵? = −3 D. lim !→#% ࠵?(࠵?) = ∞ , ࠵?(−3) = ࠵?. ࠵?. , vertical asymptote at ࠵? = −3 Q1.3 Select one correct answer. A. lim !→#& ! ࠵?(࠵?) = −5 , lim !→#& " ࠵?(࠵?) = −1 , ࠵?(−1) = −5 and ࠵?(࠵?) is continuous on the left at ࠵? = −1 . B. lim !→#& ! ࠵?(࠵?) = −5 , lim !→#& " ࠵?(࠵?) = −1 , ࠵?(−1) = ࠵?. ࠵?. and ࠵?(࠵?) is discontinuous at ࠵? = −1 . C. lim !→#& ! ࠵?(࠵?) = −1 , lim !→#& " ࠵?(࠵?) = −5 , ࠵?(−1) = −1 and ࠵?(࠵?) is continuous on the right at ࠵? = −1 . D. lim !→#& ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. , ࠵?(−1) = ࠵?. ࠵?. and ࠵?(࠵?) is discontinuous at ࠵? = −1 . Q1.4 Select one correct answer. A. lim !→’ ! ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. , lim !→’ " ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. , ࠵?(2) = ࠵?. ࠵?., and ࠵?(࠵?) is discontinuous at ࠵? = 2 . B. lim !→’ ! ࠵?(࠵?) = −∞. , lim !→’ " ࠵?(࠵?) = ∞ , ࠵?(2) = ࠵?. ࠵?., vertical asymptote at ࠵? = 2 . C. lim !→’ ࠵?(࠵?) = ࠵?. ࠵?. ࠵?. ; ࠵?(2) = ∞., vertical asymptote at ࠵? = 2 . D. lim !→’ ! ࠵?(࠵?) = ∞ , lim !→’ " ࠵?(࠵?) = −∞ , ࠵?(2) = ࠵?. ࠵?., vertical asymptote at ࠵? = 2 .

MA121A1 Test1 Fall 2023 Q5. (22 points) Open Response. MUST show work for full credit. An investment of $40,000 earns an annual rate of r %. Set up (do not compute) expressions for all parts. Q5.1 (5 points) Find the future value of the investment after 15 years if the rate is 6% and it is compounded monthly. You must obtain an expression for the future value ࠵? (do not compute). Q5.2 (5 points) Find the future value of the investment after 15 years if the rate is 6% and it is compounded continuously. You must obtain an expression for the future value ࠵? (do not compute). Q5.3 (6 points) How long will it take money invested to triple if the rate is 6% and it is compounded quarterly? You must obtain an expression for time t (do not compute). Q5.4 (6 points) What should be the rate r for the money invested to double in 15 years if the rate is compounded continuously? You must obtain an expression for rate r (do not compute). Q6. (18 points) Open Response. MUST show work for full credit. The research department in a company that manufactures clocks established the following price-demand and cost functions: ࠵?(࠵?) = 60 − 1.5࠵? , ࠵?(࠵?) = 100 + 30࠵? . Domain for both functions is 0 ≤ ࠵? ≤ 40 . Where ࠵? is in thousands of units and ࠵?(࠵?) is in thousands of dollars. Q5.1 (4 points) Find the revenue and profit functions. Q6.2 (6 points) Set up ( do not compute ) the expressions for the x-coordinate of maximum revenue and profit. Q6.3 (8 points) Set up ( do not compute ) the expressions for the x-coordinates of break-even points and based on that provide the interval(s) of loss and profit.

MA121A1 Test1 Fall 2023 Q7. (22 points) Open Response. MUST show work for full credit. Given ࠵?(࠵?) = ! # #%!#&$ ! # #(!#&’ . Q7.1 Find A. lim !→#’ ! ࠵?(࠵?) = B. lim !→#’ " ࠵?(࠵?) = C. lim !→#’ ࠵?(࠵?) = D. ࠵?(−2) = E. Vertical asymptote(s) of ࠵?(࠵?) . Q7.2 Find A. lim !→- ࠵?(࠵?) = B. ࠵?(6) = C. All the points of discontinuity of ࠵?(࠵?) . Q7.3 Find A. lim !→. ࠵?(࠵?) = B. lim !→#. ࠵?(࠵?) = C. Horizontal asymptote of ࠵?(࠵?) .