What is the third derivative of f (@) = cos (2x)? O A. 2 sin 2x O B. -4 cos 2x O C. 8 sin 2x O D. 8 cos 2x O E. -8 cos 2x 2 ? Which of the integrals is equal to lim + 4k n-+00 O A. Say x3dx O B. fordx O C. fox'dx O D. fox'dx O E. .8 r'deWhich best describes the behavior of the function f (x) = 4vr-1-4 12-21 as x approaches 2? O A. lim f (a) does not exist. O B. lim f (x) = 0 O C. lim f (x) =1 I-+2 O D. lim f (x) = 2 I-+2 O E. lim f (x) = 00 I +2What is the equation of the tangent line to f (x) = a + 2x + 4 at the point (1, 7)? O A. y = 5x - 6 O B. y = 5x + 2 O C. y= -5x + 6 O D. y=-7x-4 O E. y = 7x+4 Which of the limits is equal to f (x2 + x) de? O A. lim 2-900 2k= 1 ( 1 + #) + ( 1 + 4) ( # ) O B. lim ( 1 + * * ) + ( 1+ O C. lim 7-900 _k=1 (1+ + ( 1 + 32 ) ( x ) O D lim Uk=1 (1 4 ) 2 + ( 1+ #) ( # ) OE lim 3k 3k 7-700 Uk=1 n 12 + ( 1 + nThe acceleration a(t) of a car starting from rest is given by a (t) = 1 + 3vt miles per hour per second. What is the velocity of the car after 9 seconds? O A. 36 mph O B. 63 mph O C. 45 mph O D. 54 mph O E. 72 mphSelected values of the real-number function fare given. X 1.9 1.99 1.999 2.001 2.01 2.1 f(x) 2.470 2.647 2.665 2.669 2.687 2.870 Which is the best estimate of lim f I ? r-+2 O A. 2.000 O B. 2.470 O C. 2.667 O D. 2.970 O E. The limit does not exist.Consider the function f (x) = 2 sin x - sin 2x on the interval 0, 7]. Find the approximate value(s) of c on this interval such that f (c) is equal to the average value of f on the interval. O A. c=1 .238, c~ 2.808 O B. C 1.273 O C. C$ 1.380, c~ 2.712 O D. C$ 1.592 O E. C~ 2.094Which function is both continuous and differentiable for all x? O A. x if x 2 O B. x? if x -1 O c. f(x) = 15x -41 OD. fE -9 O E. (x - 3)' if x 32(4th) +5(4+h)-148 The expression lim h represents which derivative? h-+0 O A. f'(0) if f(x) = 2x3+ 5x - 148 O B. f'(0) if f(x) = 8x3 + 20x O c. f'(2) if f(x) = 4x3 + 4x O D. f'(4) if f(a) = 2x3 + 5x O E. f'(4) if f(x) = 8x + 20xLet fbe a function whose domain is all real numbers except 2 and whose derivative is f' ( a ) = -2 On which intervals is the function fincreasing? O A. (-00, 00) O B. (-00, 4) O C. (-0o, 2) and (2, 00) O D. (-0o, -4) and (2, 00) O E. (-oo, -2) and (4, Do)If f (a) = , which limit can be interpreted as f'(8)? O A. lim /c-8-8 1 +8 O B. lim -8 1-+8 I-8 O C. lim /c-8-2 T-8 O D. lim I-+8 I-8 O E. lim VI-2 T-+8 I-8What is the average value of f (x) = (x - 1) on [-1, 1]? O A. - O B. 0919 O C. - 09/ H O D. O E." fig(x) de = r, fig(x) dx = s, and f2 g(x) dx = t, what is f, g(x) dz? O A. r - s -t O B. rts-t O c. r-stt O D. t-r-s O E. s-r-tIf the derivative of fis given as f(x) = 6x- - 9, at which value of x does fhave a relative maximum? O A. V6 2 O B. V6 3 O C. O D. V6 3 O E. v6 2dy Find the solution of the differential equation y (@ + 1) + 0 that satisfies the initial condition y ( -2) = 1. O A. y= Vaz +2x+1 O B. y = In - O cy= 1 O D. y = In(x + 1) +1 O E. y= 1Find d sec' t dt ) . O A. 2x tan O B. tan - tan 1 O C. sec2 (x2) O D. sec - sec (1) O E. 2x sec2What does So Vx2 - 4x + 4dx equal? O A. O B. O C. O D. 2 O E. 3If the radius of a sphere is increasing at the constant rate of 3 centimeters per second, how fast is the volume changing when the surface area is 10 square centimeters? O A. 15 cubic centimeters per second O B. 20 cubic centimeters per second O C. 25 cubic centimeters per second O D. 30 cubic centimeters per second O E. 35 cubic centimeters per secondThe slope field from a differential equation is shown. Which could be a particular solution of the differential equation? 1--1-1-1 1--1- 1-- 1 1- 1 1- -1-1 -1-1- 1-1 1 1 1 1- 1- 1 1- -1-1 1-1 1-- 1 + 1 1-1 1 -- 1 1 1 O A. y = In (x) O B. y = ex O C. y = 2x O Dy =x2 O E. y = tanxThe velocity of a particle moving in a straight line at time t is given as v(t) = et. How far does the particle move from t = 0 to 3? O A. e O B. e3 O c. e - 1 O D. e3 + 1 O E. 3e3 + 1Let g(x) = 23 + 2x - 5. By the Mean Value Theorem for Derivatives, there must a number c in (-1, 2) such that g'(c) equals which value? O A. -5 O B. -2.5 O C. -2 O D. 2 O E. 5The velocity of a particle moving in a straight line at time t is given as v (t) = (t - 2) (t - 3) For what values of t is the acceleration of the particle equal to 0? O A. and 7 O B. and 2 O C. and 3 O D. 1:5/05 and 3 O E. and 3Which differential equation has y = v1 - 2 as a solution? O A. dy try = 0 O B. dy taty=0 O C. +x=0 O D. dy O E. dy + = 0The function fis continuous and hes the values shown the table. What is the best approximation of If f (3:) d1: found by using the Treoezoidel Rule: with 3 suhintewals? 0 E. 4.25 O C. 4.5 O D. 4.?5 4x-+1 if x 1 What are the values of a and b for which the function fis continuous everywhere? O A. a= -4;b=-1 O B. a= -3;b=-1 O C. a = 3;b=1 O D. a = 4;b=1 O E. a = 15;b = 4