Problem 1. (1 point) Problem 9. (1 point) Find the general antiderivative for 15 Let f (x) = = x2 + 1' dy = 616 - 413 -4. Enter an antiderivative of f(x) du y = + C. Problem 10. (1 point) Find the most general antiderivative for the function 3vx+ - Vx Problem 2. (1 point) Note: Don't enter the +C . It's included for you. Antiderivative = + C. Find the general antiderivative for dy - 5ex + 7. Problem 11. (1 point) dx Find the most general antiderivative for the function 5 =-4Vx2. Vx y= + C. Antiderivative = 2 Problem 12. (1 point) Problem 3. (1 point) Consider the function f(x) = 20x3 - 12x2 + 4x -9. Enter an anti- Find an antiderivative for 3x4 - 3x x3 derivative of f (x) Antiderivative = Problem 4. (1 point) Problem 13. (1 point) 5-4xet Find the most general antiderivative for the function 3 Find an antiderivative for the function - 3 Vu Note: Don't enter the +C . It's included for you. Antiderivative = Antiderivative = + C. Problem 5. (1 point) Problem 14. (1 point) Find the most general antiderivative for the function Find the function R that satisfies the following conditions: 84 _ 3 76-3) R'(x) = 5-0.3x; R(0) = 5. Note: Don't enter the +C . It's included for you. Antiderivative = -+ C. Problem 6. (1 point) R(x) = Let f (x) =- 4 - set. Problem 15. (1 point) Enter an antiderivative of f (x) Consider the function f(x) = 7 2 276, *20. Problem 7. (1 point) Let F (x) be the antiderivative of f(x) with F(1) = 0. Find the general antiderivative for Then F(x) = dx Problem 16. (1 point) di ~ = 61-1+7. Consider the function f(t) = 3sec2(1) -312. Let F(1) be the anti- derivative of f (t) with F(0) = 0. + C. Then F(t) equals Problem 8. (1 point) 15 Let f(x) = Problem 17. (1 point) V1-x2 Given f'(x) = 6cosx - 6sinx and f (0) = 2, Enter an antiderivative of f (x) find f(x) = Problem 18. (1 point) Problem 21. (1 point) Find the function p that satisfies the following conditions (assume Consider the function f(x) whose second derivative is f"(x) = x>0): 2x + 8sin(x). If f(0) = 3 and f'(0) = 2, what is f(x)? P' ( x) = - 70 3; P(8) = 7. f ( x) = P(x) = Problem 22. (1 point) Problem 19. (1 point) Given f"(x) = e" with f"(0) =7, f'(0) =9, Find the particular antiderivative that satisfies the following con- then f(x) = -+ C. ditions: Note that your answer should not contain a general constant. dM 512 - 3. dt 12 M(4) = 4. Problem 23. (1 point) Given that the graph of f(x) passes through the point (7, 7) and M(1) = that the slope of its tangent line at (x, f(x)) is 3x + 3, what is f(3)? Problem 20. (1 point) Find the particular antiderivative that satisfies the following con- ditions: Problem 24. (1 point) dy 5x + 2. A particle moves on a straight line and has acceleration a(t) = dx VX y(1) = 2. 121 + 12. Its position at time t = 0 is s(0) = 16 and its velocity at time t = 0 y= is v(0) = 14. What is its position at time t = 8