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B 30 C 15 D 450 E None of the above Final Exam MAC 2233 Review 1 30 lim 15 A 15 2 Which statements is are true I 7 3 5 2 3 5 is continuous at 1 II lim 2 2 2 2 III The horizontal asymptote of is 1 2 1 A I and II B I and III C II only D I only E All of them 3 Differentiate 3 7 5 10 8 35 4 10 A 3 2 6 B 7 4 5 1 C 2 35 4 8 2 7 4 10 D 3 E None of the above B 12 07 C 0 08 D 0 90 E None of the above 2 2 3 1 2 7 2 A 2 B 15 continuously Round to the nearest whole number A 10 years B 62 years C 37 years D 6 years E None of the above 4 In 2007 in the United States the cost per gallon for gas was 2 85 while in 2014 it was 3 43 Find the average rate of change of the cost per gallon for gas per year from 2007 to 2014 Round to the nearest hundredth A 0 58 5 Find the value of A that makes continuous on all real numbers 6 How long will it take for 3 000 to turn into 30 000 at an annual interest rate of 3 7 compounded C 10 D 11 E None of the above 7 How much money is in the account when 800 is invested at a 4 6 interest rate compounded monthly after 8 Find the marginal average cost given the total cost is 4 8 000 when x units are produced 10 years A 1 267 26 B 1 387 62 C 1 266 15 D 1 357 32 E None of the above 8 000 2 A 4 B C 0 D 4 8 000 2 E None of the above 9 Differentiate 4 ln 6 A 24 ln 5 24 B 5 C 4 ln 6 5 D 24 E None of the above 10 Differentiate 3 2 Factor completely A 6 2 2 B 2 2 3 C 2 3 2 2 2 1 D 2 2 3 2 E None of the above 13 Differentiate 3 2 2 5 3 Factorize Completely 12 Differentiate 2 5 4 A 2 5 4 B 2 5 C 2 5 2 5 4 D 2 5 2 5 4 E None of the above A 3 2 2 5 2 14 2 5 B 36 2 2 5 2 C 3 2 2 5 2 2 2 3 5 D 12 2 2 2 5 4 E None of the above 11 Which of the following is are true I II ln 3 III Profit Cost Revenue 3 A I and II B II and III C II only D I and III E None of them 14 Use the graph of to find the interval on which 0 A 3 0 2 3 5 15 Find all inflection points of 3 5 10 4 16 The graph of is given below Find the intervals where 0 B 2 1 3 C 2 1 3 D 3 0 2 3 5 E None of the above A 0 0 2 64 8 B 0 0 3 101 1 C 2 64 D 0 0 E None of the above A 1 5 0 5 B 1 C 1 5 1 1 0 5 D 1 E None of the above A 35 5 35 5 B 81 10 C 40 31 D 15 5 55 5 E None of the above 17 0 1 5 the critical numbers Use the second derivative test to find the x coordinate of the local extrema of the function given the second derivative 2 1 2 A Local max at 1 and local min at 5 B Local max at 1 and 5 C Local min at 1 and 5 D Local max at 5 and local min at 1 E None of the above 18 Find two numbers whose difference is 71 and whose product is a minimum 21 Which of these is are true Choose all that apply If are continuous on and is an antiderivative of then I II III ln 1 A I and II B II and III C I and III D All of them E None of them 22 Evaluate the following limits SHOW WORK FOR EACH to receive full credit 19 Evaluate 3 2 4 2 A 2 B 6 C 14 D 18 A 12 B 34 C 0 D 12 E None of the above E None of the above 20 Evaluate 6 7 ln 34 12 12 a lim 7 2 1 b lim 25 25 5 c lim 3 2 7 1 6 2 8 d lim 5 5 6 10 e lim 4 3 4 23 Use the graph to answer the following questions a lim 6 b lim c lim 1 d Is continuous at 2 Why or why not e Is continuous at 1 Why or why not 5 2 4 5 24 Find the horizontal and vertical asymptotes of using limits Failure to use limits will result in a zero State if there are any holes in the graph and if yes give the coordinates 25 Use the definition of the derivative four step process in book to differentiate 5 Any other method of finding the derivative will result in a zero 26 Let 2 3 3 2 12 4 a Find the equation of the tangent line in slope intercept form when 1 b Find the x values where the tangent line is horizontal 27 Differentiate a 4 3 5 2 7 b 5 2 7 10 4 28 A function is continuous at a value if the following conditions are met 1 is defined 2 lim 3 lim Use the three conditions of continuity to decide if is continuous at 3 2 1 3 5 3 2 4 3 1 2 3 29 The profit function in dollars for a company producing units of facemasks is given below Find P 30 and P 30 and interpret your results using words 5 2 100 3000 30 The revenue when x units of a certain commodity are sold is given by 36 2 7 200 0 100 a Find the actual revenue of producing the 61st unit b Use marginal analysis to estimate the revenue of the 61st unit 31 A 700 grams sample decays exponentially continuously and after 50 years 200 grams is left a Find the rate of decay Round to five decimal places b How many grams are left after 80 years Round to the nearest whole number 32 Find the equation of the tangent line in slope intercept form of 3 6 3 4 0 33 Differentiate the following functions 3 2 5 3 1 5 7 ln factorize final answer completely for full credit a b c ln 3 2 2 34 Find the x values where the tangent line is horizontal …

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