0_2022sp3.pdf x Dashboard X + ads/mas120_2022sp3.pdf 1 / 18 100% +8 MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 1. [4 marks] Evaluate the following limits using calculus and showing all working. . [7 marks] 2 + 2x - 3 (a) lim (a) Sketch the graph of f(x) = VI. 2 +1 22 -1 (b) 4x - 1 + 30 2-190 20(1 - 12) (b) Using translations and reflections, sketch the graph of g(x) = 1 - -(4 -r), showing and labeling intermediate sketches. 2. [4 marks] Find the domain, giving reasons, of the function f(x) = (e* -1)-1/2 and express your answer using the interval notation. Activate Windows Goko Settings to act vate Windows. nas120_2022sp3 f....pdf Show O g 20 0 Cloudy ~ 9 0 5 ( 1) 12:05 PM 11/30/202mas120_2022sp3.pdf x Dashboard kino/Downloads/mas 120_2022sp3.pdf 3 / 18 - 100% +HO MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 4. [9 marks] Find for the following, showing all working: 5. [12 marks Using calculus and showing all your working, sketch the function f(x) = 2+1 (a) y COS ( T ) 12 - 9 noting the domain of f(z), any intercepts or asymptotes, regions where the function is increasing or decreasing and any relative extrema. (b) y = 21n sin(2x) ( c ) 3x y + Vity - ev Activate Windows Go to Settings to betoare Wiregane Show all 12:05 PM GDE mas120_2022sp3 f.pdf 20'C Cloudy ~D E ( )11/30/2022 arch OD Fir X mas 120_2022sp3.pdf * *Dashboard X + Users/kino/Downloads/mas120_2022sp3.pdf 5 / 18 - 100% +8 1 6 MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 (Question 5. continued. ..) . [6 marks] Find, using calculus and showing all working, the absolute maximum and the absolute minimum of the function f(x) = 24 - 182 + 5 for r E [-2, 4). Activate Windows Go to Settings to activate Windows. Show all D 12:05 PM con mas120_2022sp3 f.pdf 20.C Cloudy ~ [ ( 4) 11/30/2022 searchx mas120_2022sp3.pdf x Dashboard + V ers/kino/Downloads/mas120_2022sp3.pdf 7 / 18 100% +| 8 MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 7. [8 marks] Find the following indefinite integrals: 8. [8 marks] Find the following definite integrals, using calculus and showing all working: (2) ( 212 - 2)et/2 dr (b) 2Valid ( b) ( It be a de . Activate Windows Go to Settings to activate Windows, Show all 12:05 PM mas120_2022sps f....pdf 20.C Cloudy ~ DI E (6 4) 11/30/2022 O chx mas120_2022sp3.pdf X Dashboard + sers/kino/ Downloads/mas 120_2022sp3.pdf 9 / 18 - 100% MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 9. [4 marks] As an exercise ball is inflated, its radius increases from 40cm to 4lem. Using linear approximations estimate the change in volume of the ball. (The volume of a sphere of 11. [9 marks] Find y(x) for the following: radius r is V - -773 (a) dy e (3.1 1) with y(0) = 0 10. [5 marks] An ice-cube with 3cm sides is placed in a warm drink and starts to melt with the side length decreasing at a rate of 1mm per minute. At what rate is the volume of the ice-cube melting when its side length is 2.5cm? (b) zy -24 3.x2 with y (1 ) = 1 Activate Windows Show all CDB mas 120_2022sp3 f...pdf 12:05 PM 20'C Cloudy ~0 0 409/30 2022 o searchMAS120 Fir X mas120_2022sp3.pdf x Dashboard C:/Users/kino/Downloads/mas120_2022sp3.pdf sp3.pdf 11 / 18 100% + MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 12. [6 marks 13. [12 marks] A cook has finished baking a cake and placed it on the bench to cool. The temperature in the room is 20'C and the temperature of the cake when it was taken out of (a) Using the trapezoidal rule with n - 4, estimate the integral e at da . the oven is 160 C Given that the temperature of the cake is governed by Newton's law of cooling, write down a differential equation governing T(t), the temperature of the cake after t hours. What is the appropriate initial condition? (Newton's law of cooling: _K(T - Ta), where K is a constant and To is the ambient temperature.) (b) From you answer in part (a), derive the solution T(t) = 20 + 140e Kt, where K is a constant. (b) Calculate the exact result and compare this with the approximate answer in part (a) 10 by calculating the absolute error. Activate Windows Go to Settings to activate Windows. Show all 11 mas120_2022sp3 f....pdf 12:06 PM 20.C Cloudy ~ D O E ( 4) 11/30/2022 here to search OOMAS120 Fir X S mas120_2022sp3.pdf x Dashboard x + X ile | C:/Users/kino/Downloads/mas120_2022sp3.pdf 2sp3.pdf 13 / 18 - 100% + 83 MAS120 - Applied Mathematics Final Examination - SP3 2022 MAS120 - Applied Mathematics Final Examination - SP3 2022 (Question 13 continued. ..) (5 marks] Using calculus and showing all your working, find the area between the curves f(x) - 4VT and g(2) = 12. (c) Given that the cake has cooled to 90 C after 1 hour, determine the constant K (d) The cook decides that the cake is cool enough to be taken out of the cake pan when its temperature lowers to 40 degrees C. Find when this will happen, both in exact form and as a decimal approximation to at least 2 decimal places, showing all working. 15 . [4 marks] Find the volume of the solid of revolution formed by rotating f(r) = Itz about the r-axis for 1