5. Evaluate the following definite integral Si (2x + Vx -1) dx. c. 1 d. 3 e. 3 a. 6. Find the area bounded by the curve f (x) = x2 - 5x and the straight line g (x) = -2x. 23 a. b. C. 5 NIW e. 11 NI 7. Evaluate the following integral by using integration by parts S (3x2e2x) dx $2x ( 3 x 2 + 3 x + ; ) + c b. - (3x2 - x+ 3)+ c c. ezx ( C. 2 (x2 - 2x + ; ) + c d. e 2x (3x2 - 3x +;) + c e. ex (3x2 - 3x + + c 8. Use partial fraction decomposition method to evaluate the following integral. 4x2+ 2x -6 x(x - 3) (x + 1) dx a. 2ln|x| - In|x - 3| + In|x + 1| + c b. 2ln|x] - In|x - 3| + 3ln|x + 1| + c c. 2ln|x| + 3ln/x - 31 -In|x + 1| + c d. 3ln|x| - 3In|x - 3| + In|x +1/ + c e. 2ln|x| + In|x - 3| + 3ln/x + 1| + c 9. Given f(x) =2 --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 (5, too).10. Evaluate the following integral (e2x - cos2x + 2) dx e 2x sinzx + 2x + c a. 2 2 b. 2e2x - 2sin2x + c d. e2x - sin2x + 2x + c 2 Ce2x _sin2x _ 2x + C . 92 + sinzx + 2x + c 2 11. Which of the following integral do we get if we substitute Inx = u ? In2 xVinx X dx a. fuvudu b. frudu c. fouvudu d. fit du e. fourdu 12. Suppose that fee J r dx = 1. Find S, ex In x dx in terms of I. a. 1+1 be + 1 c. 1 - I d. ee - I e. e - I 13. Evaluate the following integral by using substitution method xe *2 dx =? N a. + c b . x tex + c C. ex + d. ex + c exz e. 2 + c 14. Given that the derivative of f is f'(x) = . On which interval is f is concave down ? a. (-00, 0) b. (, +00) C. (0, +00) d. (1, too) e. (-1, +00) 15. Given (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 = -3. Find a. 15 a. 6 b. C. -9 d. 9 e. None of them B17. An equation of the tangent line to the curve y = 4x at x = 1 is c. 5x - 8y - 4 = 0 a. 9x - 8y +4 =0 b . 8 x - 2y + 3=0 e. 8x - 9y + 4 = 0 d. 8x + 9y - 4 =0 18. Find the absolute max value for the function f(x) = 4x3 + x2 - 3x - 4 on the interval [-4,2] a. 5 b. =10 d. 3 e . c. 0 19. If 3x2 - 2xy + y2 = 2, then ax 2x+2y a. 3x + 2y b . 3x-y 3x+ y dy-3x e. x+3y 2x -2y C. xty y - x 20. Find Vx+1-2 lim X-+3 x - 3 1 e. 4 a. b. C. A IP d. - 21. Consider the following improper integrals. 1. L12dx I1. (1 1 dx One of the following statements is true. Which one? a. I. is convergent, II. is divergent. b. I. is divergent, Il. is divergent. C. They are all divergent. d. They are all convergent. e. I. is divergent, Il. is convergent. 22. Evaluate the improper integral. 8 esx dx a. b. 0 C. UIIN d. e. The integral diverges. BCYPRUS INTERNATIONAL UNIVERSITY CIU MATH 101, Calculus I, 2021-2022 Spring Semester CYPRUS IHT CANATIONAL Name Final Exam Duration: 75 min. UNIVERSITY No: Halil Gezer Grol,02, Gr4; Zalihe Yarkiner Gr03, Gr05; Cemalive Kurt Gr06 1. Given the limit B lim = A Which of the following is NOT correct for the given limit? a. If f (x) = ex then A = 0o . b. If f (x) = Inx then A= 0. c. If f (x) = x+1 then A = 0. d. If f (x) = 2x2 + 3x +1 then A = 2. e. If f (x) = x3 + 1 then A = 0. 2. Given f' (x ) = x4-4x2 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 max at x = -2. c. The local max value is 0. d. There is a local max at x = 2. e. There is a local min at x = 0. 3. Given f' (x) =3x2 - 4x+1 If f (1) = 2, then find f (2) =? a. -2 b. 5 C. 4 d. 1 e. 3 4. Given Which of the following integral do we get if we substitute x = sinu ? du a. So sinudu b. S2 - Jo sinu c. S2 - cosu 1 sinu du d. Jo cosu e. Sz du