\fWhich integral can be represented by lim x 1 sin (5Ck:) 4x, where cx is chosen arbitrarily in the kth n-+00 subinterval and Ar = -0? O A. So sin' (x) da O B. So sin (5xx)dx O C. So sin (5x) dx O D. So sin (xx) dx O E. S, sin (rx) daUse four rectangles to approximate 2 + 3) du using the midpoint rectangular approximation method (MRAM). O A. 3.94 O B. 4.35 O C. 4.94 O D. 5.35 O E. 5.94What is an antiderivative of f (2) = cosx + I O A. F (@) = cos + Inx +C O B. F(x) = - cost+ + 0 O C. F(x) = sinc + + 0 O D. F(x) = sinc + In|>| + C O E. F(x) = - cosx+ Inx + CWhat are the local extrema of g (x) = Jo (12 -6t + 8) dt? O A. g has a local maximum at x = 2 and a local minimum at x = 4. O B. g has a local maximum at x = -2 and a local minimum at x = 4. O C. g has a local maximum at x = 4 and a local minimum at x = 2. O D. g has a local maximum at x = 4 and a local minimum at x = -2. O E. g has a local maximum at x = -4 and a local minimum at x = -2.What is the antiderivative of f (x) = 3x - 2,c? O A. F(x) = 3x - 1 1 + C 212 O B. F(x) = 3x2 - 19 191 - + 0 O C. 3x2 2 + 0 O D. F(x) = 2 + 0 O E. F(x) = 4x 2 2 + CThe acceleration of an object is given by a (t) = cos (at). The velocity of the object at time t = 0 is 2 TT Which expression can be used to find the total distance traveled in the first seconds? O A. + sin (at) ) dt O B. 11 So (cos (nt) + =) dt O C. li (4 + sin (at)) dt + 1" # (7 + sin (at))dt 11 O D. 11 + sin (at) ) dt + J. + sin (at) ) dt O E. So 5+ sin (at) ) dt + J + sin (at) ) dtWhat is the average value of the function f (x) = Inc on [1, 4]? O A. 0.3034 O B. 0.3203 O C. 0.3402 O D. 0.3624 O E. 0.3802What is the area of the region bounded by y 2 11:2, 1;: U, :1: = 1. and x = 2\"? ORE OBS If fif(x) de = 7, what is S? (f (x) + 4x) dx? O A. - 73 2 O B. 32 - 2 O C. 31 2 O D. 33 2 O E. - 31Find lim 2ex-2-2x-12 O A. 0 O B. O C. O D. colts O E. DOFor what values of x on the interval [-3, 3] does the function f (@) = 9 - x equal its average value? O A. = -6, x =6 O B. x = -3, x = 3 O C. x= - V6, x = V6 O D. x = -V6, x = V3 O E. x = - V3, x = \\3The velocity function, in meters per second, for a particle moving along a line is given as v (t) = t- - 2t . What is the total distance the particle travels from t = 0 to t = 3? O A. 0 meters O B. meters O C. meters O D. 2 meters O E. 05 00 metersWhat is the differential equation for the slope field in the following graph? 1 * 13 -2- -3- O A. di =y-c O B. dy di =c-y O C. dy =y- 2- O D. dy O E. = yz - 12The population of a country doubles every 20 years. If the population of the country were 100 million in 2000, which best approximates the population in 2015? O A. 157 million O B. 162 million O C. 168 million O D. 174 million O E. 180 millionApproximate Jo av/3 - xdax using the Trapezoidal Rule with four subintervals of equal length O A. 3.68 O B. 3.75 O C. 3.96 O D. 4.10 O E. 4.312 Evaluate O O A. 1.25 O B. 1.31 O C. 1.43 O D. 1.52 O E. 1.64\fIf $1,000 is put into a savings account at 8% interest compounded continuously, how much will it be worth at the end of 4 years? O A. $1,360.49 O B. $1,372.79 O C. $1,375.67 O D. $1,377.13 O E. $1,388.19dy What is the shape of the graph of the general solution of the differential equation = y? O A. straight line O B. parabola O C. hyperbola O D. exponential curve O E. logarithmic curveSilver 108 is a radioactive isotope that decays at a rate proportional to the amount present and has a half Iife of 418 years. Ifthe original amount present of silver 1138 were 100 grams. how much would be left after 100 years? O A. T845 grams O E. 813?? grams O C. 84.?2 grams O D. 88.21 grams O E. 92.68 grams Evaluate / (sina + cos r cot x) dx. O A. cota+ C O B. - cote + C O C. - sec'x + C O D. - 09 / P cscr + C O E. Toscax + CSuppose a colony of bacteria grows exponentially with a growth rate constant of 0.25. If the colony contains 6,000 cells now, approximately how many did it contain 4 hours ago? O A. 1,500 O B. 1,717 O C. 1,956 O D. 2,075 O E. 2,207