5. ax = NI- (1- x2 A. tan x + C B. sin x + C O C. sec | x | + C D. none of these dx 6. x (x2 - 1) 2 A. sec | x | + C O B. cot x + C C. tan x + C O D. none of these9. If f ( x ) = sin (2x), then f '( x) would be O A. -2 sin (2x) OB. 2 sin( 2 x ) O C. 2 V1 - 4x OD. V1 O E. none of these 10. If f( x) = tan" (e *), then f '( x) would be O A. 2 1+ e 4 X B. 202 x 1+ ex O C. 282 x 1+ 2-2 x 1 OD. 1+ (e2 x )2 E. none of these11. Find the derivative of the function f(x) = sinh (4x). O A. f'( x) = cosh (4x) O B. f'( x) = 4 cosh ( 4x) O c. f'( x) =-4 cosh ( 4x) O D. f' ( x) = -cosh (4x) 12. Find the derivative of the function f(x) = In(sech (2x)). O A. f'( x) = -2 tanh (2x) O B. f' ( x) = -tanh (2x) O c. f'(x) = 2 tanh(2x ) sech( 2 x ) O D. f ' ( x) =-2 sech2(2x)\f16. The half-life of radium-226 is 1590 years. A sample has a mass at 100 mg. Find the mass after 1000 years. A. 30 mg B. 40 mg C. 55 mg D. 65 mg 17. It $1000 is invested at 6% interest, compounded annually, what the value of the investment after 3 years? A. $1191.02 B. $1201.25 C. $1181.32 D. $1191.45 19- Which of the following is a general solution of the differential equation d1 = dx ex 2 B+ex A. y=|n[eX(6+eX)+C B. y=6+eX+C X C. y= B-I-ex D. y=|n(6+eX)+C 20. It 50 grams ot a radioactive substance decomposed to 42 grams in 2 years, then, to the nearest gram, the amount left after 5 years would be A. 30 grams B. 32 grams C. 22 grams D. 40 grams 21. Which of the following is a general solution of the differential equation 2% = dx . CO O A. y= 3 X + C 3 O B. y= RX3 + C O C. y = $3 x + C O D. y = x + C 22. Which of the following is a general solution of the differential equation dy = x 6x2 . CO 2y + cos y O A. y + sin y = 2x5 + C O B. y - 2 sin y = x + C O C. y= 12x3 + sin y + C O D. y = 2 cosy + 2x3 + C23. Which of the following is a general solution of the differential equation y' = x y? A. y= 3 - X + C O B. y = Ces O C. y = es + C OD. y = p x 3 13 + C 24. Which of the following differential equations is not separable? OA. dy = x+y dix OB. dy = xy dx O C. dy _ x dix O D. dy = 2 y dx25. Find the solution of the differential equation dy - x + 1 that passes through dx the point (-2, 2). O A. y= -x2 + x + 4 1/2 OB. y= N IW x2 + 2 O C. y= x2 + 3x+8 O D. y= 1 x2 + X +8 E. none of these 26. Find the limit: lim In x X- 1 x - 1 OA. O OB. 1 O C. 0.5 OD. -1\f29. Find the approximate area of the region bounded by the curves y = x - x and y = 3x. O A. 7.0 O B. 7.6 O C. 3.8 O D. 8.0 30. Find the approximate area of the region bounded by the curves y = sec and y = 8 cos x on the interval - * *. O A. 17.32 O B. 8.67 O C. 9.86 O D. 10.3931. Find the approximate volume of the solid obtained by rotating x = 2J7: x = 0, y = 9 about the yaxis. A. 508.94 B. 610.22 C. 162.0 D. 324.1 32. Find the approximate volume of the solid obtained by rotating the region between y = x4, y = 0, and x =1 about the line x = 2. A. 1.47 B. 0.47 C. 2.09 D. 0.67 33- Find the approximate length at the curve y = |n(sec x), O S x S g. A. 0.41 B. 0.88 C. 2.76 D. 0.58 2 34- Find the approximate area of the surface obtained by rotating x = (y + 1 3 2)3/2, 1 s y s 2 about the X-axis. A. 32.99 B. 10.5 C. 5.25 D. 16.49 35. An object is moving along the coordinate line with velocity v(t) = 5 cost, 0 dx O B. W = [ " F ( x ) dx O c . W = ( b - all " F ( x ) dx OD. W = [ " F 1 x ) dx43. According to Hooke's Law, the Force needed to displace a spring x units from its natural length is given by which equation? A. F(x)=x+k B. F(x)=k"' C. F(x)=kx D. F(x)=kx2 44. Suppose that a Force of 20N stretches a spring 0.4 m beyond its natural length. How Far will a 40N force stretch the spring? A. 1.0 B. 0.4 C. 0.2 D. 0.8 45. A cylindrical tank of about 8 m high, with a radius of 3 m, is filled half way with water. Approximately how much work is needed to pump the water to the rim of the tank? O A. 6.650 x 10 Nm O B. 8.867 x 10 Nm O C. 6.788 x 10 Nm O D. 2.217 x 10 Nm O E. none of these 46. Consider the region, R, bounded by the x-axis, the y-axis, and the graphs of the equations y = 2 + 1 and y = In x. Find the area of the region R. O A. 5.497 O B. 1.483 O C. 0.879 O D. 0.01347. Consider the region, R, bounded by the y-axis and the curve y = x for 0 s x