4. Let x(t) = t3 - 4t2 + t and y(t) = t2 - 6t + 3. Find followings at t = 1. a. x(1) b. y(1) C. dx at t=1 d. ay at t= 1 e. dy axt= 1 5. Find the area of the parallelogram shown below. 10- 6. An object moves with velocity as given in the graph below (in ft/sec). How far did the object travel from t = 0 tot = 15? 10+ velocity (fr/sec) 5 10 15 20 25 30 35 40 45 time (sec)7. Find the value of the summation. 19 cos(nk) K= 0 8. Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1= 8, A2=3, A3=1 and A4=1. y=f(x) V = [of ( x) dx At A3 10 3 5 A4 A2 (figure is NOT to scale) 9. Let A(x) = ], f(t) dt, where f is the function given by the graph below. Find A(3) and A(8) 2 3 -3 Numbers 10-16 multiple choice. Select the best possible choice. Work not needed. No partial credit. 10. The integral J d(3*) dx -evaluates to: 3X (a) x + (b) 3* + C -+C (d) 3* . In 3 + C (e) None of the above. 11. If lim f(x) = 4 and lim f(x) = 4 then --- (select all correct answers) x--9 x--9+ (a) lim f(x) = does not exist (b) f(-9) = 4 (c) lim f (x) = 4 (d) f(x) does not exist x4-9 (e) None of the above.12. Find the limit if it exists. x- + 5x - 24 lim x+3 x - 3 (a) -5 (c) 2 (d) 0 (e) 3.3 (f) 11 (b) DNE (g) None of the above. 13. lim B(2+h) -8(1) - is h+0 h (a) 0 (b) = H NIN (c) 1 (d) The limit does not exist. (e) It cannot be determined from the information given. 14. Let f be a function such that lim )-7 035 h-0 h Which of the followings must be true? (a) f is continuous at x = 3 (b) f is differentiable at x = 3 (c) The derivative of f is continuous at x = 3 (d) f can be integrate at x = 2 (e) The area under the curve f around x = 3 is 5 15. Given the graph of f(x), find J_ f(x) dx using formulas from geometry. (a) 4.5 (b) 6 (c) 13 (d) 5 (e) 0 (f) None of those