5. Evaluate the following definite integral S, (2x + Vx + 1)dx. e. 68 NI- 3 b. c. 2 d. a. 6. Find the area bounded by the curve f(x) = -x2 - 3x + 2 and the straight line g (x) =-2x. e. 11 6 b. NIOT a 7. Evaluate the following integral by using integration by parts S(3x2ezx) dx a. 2 (3x2 + 3x +; ) + c b. ezx (3x2 - x+ 3) + c c. = (x2 - 2x + 2 ) + c d. e 2x (3x2 - 3x + ;) + c e . 2x (3x2 - 3x +;) +c 8. Use partial fraction decomposition method to evaluate the following integral. 4x2+ 2x -6 x (x - 3) ( x + 1 ) dx a. 2In|x] - In|x - 3| + 3ln/x + 1| + c b. 2In|x] - In/x - 31 + In/x+1/+c c. 2ln|x| + 3ln|x - 3| - In|x + 1/ + c d. 3ln|x| - 3ln|x - 3| + In|x +1/ + c e. 2ln|x| + In|x - 3| + 3ln|x +1| + c 9. Given f (x) = 3 - 2x + 1. Which of the following is NOT correct for the given function. a. There is a Local max at x = -1. b. Local max value is 0. c. There is a Local min at x = 2. d. There is an inflection point at x = = e. Function is concave up on (, +co) A10. Evaluate the following integral [(e 2x + cos2x + 2) dx sin2x + 2x + c b. Ze2x - 2sin2x + c 3. c. S exx d. exx - sin2x + 2x + c ezx 2 sin2x 2 sinzx _ 2x + c 2 -+ 2x+c 11. Which of the following integral do we get if we substitute Inx = u? ( InxvInx X -dx a. huvudu b. Spudu c. So Vudu d. find eldu e. So uzdu 12. Suppose that , x feedx = 1. Find Sex In x dx in terms of 1. bee - 1 a. 1+1 C. 1 - I d. e + 1 e. e- I 13. Evaluate the following integral by using substitution method xe *2 dx = ? pxs + c b. x+ ex's + c C. ex + c a. d. ex + c ex? e. - + C 14. Given that the derivative of f is f'(x) = . On which interval is f is concave down ? a. (-00, 0 ) b. (, too) c. (0, +00) d. (1, too) -e. (-1, too) 15. Given f(x) = -x3 +12x + 7 . On which of the following interval is f decreasing? b . (-00, 0) b. (-00 , 2 ) c. (-2, too) d. (-00 , - 2 ) U (2, 00 ) e. ( - 2 , 2 ) 16. Given that f(x) = x3 + ax2 + 3x + 1 has an inflection point at x = -2. Find a. a. 6 15 b. 7 c. 1 d. -2 e. None of them A17. An equation of the tangent line to the curve y = 1x atx = 3 is c. 25x - 8y + 36 = 0 a. 3x - 25y - 3 = 0 b . 8 x - 25y + 36 = 0 e. 3x - 5y - 6 =0 d. 8x + 25y + 3 =0 18. Find the absolute max value for the function f(x) = 1x3 + x2 - 3x - 4 on the interval [-4,2] a. 0 b. -10 c. 5 e. 3 19. If 3x2 + 2xy + y2 = 2, then dx a. 3x + 2y 6x+2y 2x+2y b. 3x+3y 3x+y e. - 2x-2y C. x+y 2x+2y x+3y 20. Find 3 - V2x + 3 lim x-3 x2 - 3x a. CO IN b . C.- d. - e. - 18 21. Consider the following improper integrals. 1. 1 xz dx 11. One of the following statements is true. Which one? a. I. is convergent, II. is divergent. b. I. is divergent, II. is divergent. c. I. is divergent, II. is convergent d. They are all convergent. e. They are all divergent. 22. Evaluate the improper integral. e 5x dx a. b . UI IN C. d. e. The integral diverges. ACIU CYPRUS INTERNATIONAL UNIVERSITY CYPRUS MATH 101, Calculus I, 2021-2022 Spring Semester INTERNATIONAL Name Final Exam Durat UNIVERSITY Duration: 75 min. No : Halil Gezer Gr01,02, Gr4; Zalihe Yarkiner Gr03, Gr05; Cemalive Kurt Gr 1. Given the limit lim() *2 ) = A Which of the following is NOT correct for the given limit? a. If f (x) = ex then A = co . b. If f (x) = Inx then A = 0. c. If f (x) = sinx then A does not exists . d. If f (x) = 2x2 + 3x + 1 then A = 2. e. If f (x) = x+1 then A =0. 2. Given f' (x ) = 4x2-x4 Which of the following is Absolutely correct for the given function f(x) ? a. There is a Local Max at x = 0. b. There is a Local Min at x = 0. c. The local min value is 0. d. There is a local min at x = 2. e. There is a local min at x = -2. 3. Given f' (x) =3x2 - 4x+1 If f (1) = 3, then find f (2) =? b. 5 C. 4 e. 2 a. -2 d. 1 4. Given dx Jo Vitx2 Which of the following integral do we get if we substitute x = tanu ? du a. So sinudu b . SA - du sinu 0 cosu sinu 1 sinu du e. 4 -du cosu cosu