n 1. If y=e kx , then d y = n dx a. n!ekx b. nnekx c. nkekx d. knekx 2. The region of the xy plane is bounded by y= ln ( x) x for x = 1 and x = 4. The curve is rotated around the x-axis to form a solid. What is the volume of the solid generated? a. 4 ln 3 b. 4 ln 3 c. 4 ln 3 3 d. 4 ln 3 3. The average value of (ln x)5 on the interval [2, 5] is: a. 0.584 b. 1.299 c. 3.896 d. 11.687 4. A is an area surrounded by y = sin x and y = cos x for 0 x 4 . A volume is generated when revolving A around the line x = 4. Calculate that volume generated: a. 9.715 b. 4.857 c. 1.793 d. 0.897 x f ( x )= cos u 4 du 5. A function f is defined as 0 . It sits on a closed interval of [0, 1.5]. f has a local maximum of : a. 0 b. 1.120 c. 1.571 d. 1.473 6. f ' ( x )=cos ln ( x+1) 4 and f ( 0 )=2, thenf ( 3 ) = a. 4.919 b. 2.919 c. 0.919 d. -4.919 7. A rail gun shoots a projectile in a straight line with acceleration a and in a(t) = 3 - 2t. If the projectile from the launcher reaches a velocity of 10 at t = 1, and if s(t) is the distance of the projective from the rail gun at time t, then s(5) - s(1) = time t as defined by the equation: a. (10/3) or 3.334 b. (20/3) or 6.667 c. (40/3) or 13.334 d. (80/3) or 26.667 8. What is the result of : a. 9 2 x tan +C 3 9 b. x 9 tan 2 +C 9 c. 9 x tan 2 +C 2 9 d. 9 x tan 2 +C 3 9 x x sec2 9 tan 9 dx 9. Determine if the sequence an = 5 n2 4 n+1 is increasing, decreasing, neither (assuming n = 1, 2, 3...): a. Increasing b. Decreasing c. Neither d. Converges to 0 10.Determine the limit of the following sequence: 1, 2, 3, ...) a. b. 2 c. 1 d. 0 an =2 nsin n assuming n = 11. Estimate ln(2.95) using Mclauren Series: a. 2.037 b. 1.983 c. 1.081 d. 0.985 12.Determine if the sequence n2 en converges, diverges or neither: a. Converges on e b. Converges on 0 c. Diverges d. Exponentially diverges 13.Integrate the expression x ln 2 1 x dx a. cos(ln x) + C b. (ln x) + C c. arcsin(ln x) + C d. tan x + C 14.Integrate the expression a. xln |e x 1|+C 2 e x2 dx x b. e 2 x +C c. -2 x d. x e +C 15.Calculate the area bounded by the curves f(x) = cos x and g(x) = x 4: a. 8.889 b. 2.135 c. 4.560 d. 6.602 16.Find dy dx for xe x a. b. e +C c. ex x +e ln x x d. e ln x+C x x y=ln x e x x for 0 \f\f\f\f\f\f\f\f\f\f\f