1. (01.02 MC) The number of visitors to a theme park is measured during operating hours. The table shows the number of visitors, v(t), at t hours in one day. For which time of the day is the rate of change of visitors expected to be the largest, based on the data? (10 points) t, hours 11 a.m. 12 p.m. 1 p.m. 2 p.m. 3 p.m. v(t), number of visitors 12,500 15,000 24,000 21,600 19,400 11:15 a.m. O 12:33 p.m. O 1:30 p.m. O 2:10 p.m. 2. (01.02 LC) For the function y(1)= 2 . as t approaches 2, y(t) approaches . Which of the following applies? (10 points) O y 4 = 2 O y( 2) = 3 O lim y(t) =3 O lim y(t) = 2 3. (01.03 MC) The table shown gives selected values of x for the function h. X 5 5.9 5.99 5.999 6 6.01 6.1 7 h(x) -7010 -7001 -7000.5 -7000.01 100 7000.01 7000.5 7001 7010 Which of the following statements is true, based on the information in the table? (10 points) lim h(x) =7,000 and lim h(x) = -7,000 X-6- x-6+ lim h(x) = 100 lim h(x)= -7,000 and lim h(x) =7,000 X-6- lim h(x) = 64. (01.04 MC) -x2 - 3 if x 0. 12 if x = The value of im (x) is (10 points) O - 2 2 O does not exist 5. (01.04 HC) The function f is defined by (x)= 1 s 1_, Simplify lim (x) using limit theorems. (10 points) O lim (x + 1) lim ( -1) lim (x2 + x) lim ( 1 - x ) O lim (x2 -1) lim (1+ x) 6. (01.07 MC) Let g(x)=sinTX, and h (x) = 2x# + x5 - 31x2 - 57x - 28. If f is a function such that h(x) s f(x) s g(x) for -3 3 Of(x ) = Vx+3 9. (01.09 MC) 5 x+ 2 ' If the function j is represented by j(x)= 2*-3, then which of the following statements is true? (10 points) lim j(x) =00 lim j(x) =00 x-+2 and 2" lim j(x) = -co and lim j(x) = -co x 2 x_ 2 lim j(x) =-0o lim j(x) = co and lim j(x) =00 lim j(x) = -co X- - and 210. (01.10 MC) The table shows selected values of t for the continuous function f(t). -2 -1 0 f(t) -11 3 -4 7 In the interval [-2, 1], what is the fewest possible number of zeros of f? (10 points) O Zero O One O Two O Three1. (01.03 HC) x+12 Let fbe the function given by f(x)=2. x +25x+155 Part A: Graph the function fusing graphing technology. What is an appropriate horizontal scale and vertical scale for the viewing window? (5 points) Part B: Find gym or explain why 315'\") does not exist for each of the values c = 12, 13, and 14. Make sure to include reasoning using correct limit notation. (25 points) 2. (01.08 HC) The amount of income tax, t, an individual owes is defined by piecewise function t(/) and is based on the individual's income, where i is taxable income in dollars. 0.10/ if OSis 12,000 t(i) = 755 +0.12(/ -11000) if 12,000 32,000 Part A: Show that the function t() is not continuous at / = 12,000. (10 points) Part B: Find the value of constant b that makes t() continuous at / = 32,000. (20 points);3. (01.09 HC) Let g be the function given by g(x) =- (2x -3)2 4x2 -4x -3 Part A: Does the graph of g have a vertical asymptote? If so, write its equation and describe the behavior of the graph of g as it approaches the asymptote on either side. Show your work and make sure to use limit notation. (15 points) Part B: Does the graph of g have a horizontal asymptote? If so, write its equation and describe the end behavior of the graph of g. Show your work and make sure to use limit notation. (15 points) Part C: What is the range of g? Make sure to take any removable and/or non-removable discontinuities into account when finding the range of g. (10 points)