Can you please help me solve the questions that are circled. Thanks so much and have a great day:)

SECTION 2.5 Indeterminate Forms 95 212 - 9x - 5 9. lim x - 25 10. lim (Ith) - 1 37. If the mass of the ball is one kilogram and it is launched upward with an initial velocity of 60 m/sec, then 2r + 1 11. lim 1 - x 60k - 9.8 In (9% + 1) Im- 2r + 3x + 1 12. lim 1-3 X2 - 9 H () = 13lim 3x- - 4x - 4 Estimate the maximum height without air resistance by investigating 2r2 - 8 14. lim (3+h) - 27 im H(k) numerically. 15. lim (h + 2)2 - 9h 16. Tim 38. If the mass of the ball is 500 grams and it is launched upward with an 1--0 4' - 1 h - 4 initial velocity of 30 m/sec, then 17. lim - Vx - 4 1-16 x - 16 18. lim 21 + 4 15k - 2.45 In (2494 + 1) 1--2 12 - 3/2 H (k) = (h + 2) y+y - 12 Estimate the maximum height without air resistance by investigating 19. 20. lim -3 y3 - 10y + 3 im H () numerically. V2th - 2 39. GU Use a plot of f (x) = - x - 4 21. lim 22. lim Vx - 4-2 Vx - V8 _ to estimate lim f(x) to x - 8 two decimal places. Compare with the answer obtained algebraically in 23. lim 24. lim V5 - x - 1 Exercise 23. FAST - V8 -x 1-+4 2 - VX 40. GU Use a plot of f (x) = = VI - 2 x -4 * 4 10 estimate lim f (x) 26. lim numerically. Compare with the answer obtained algebraically in Exercise 25. 27. lim - col x cote 1-0 CSC x 28. lim b' - 1 B- E csc 0 41. Show numerically that for b = 3 and b = 5. lim .X - appears to equal In 3 and In 5, respectively. 29. Iim (- 1-7) 30. lim - sin x - Cos x tan x - 1 42. Show numerically that for b = 2 and b = 4. lim b" - 1 1+0 appears to 221 + 2' -20 equal In 2 and In 4, respectively. 31. lim 2' - 4 32. lim ( sec e - tan e) In Exercises 43-48, evaluate using the identity a' - b' = (a -b)(a + ab+ b?) 33. lim e- ; tan e - I tan2 0 - 1 43. lim - 8 44. lim x3 - 27 2 cos x + 3 cos x - 2 1-2 x - 2 1-+3 x2 -9 34. lim 2 cos x - 1 x2 - 5x +4 45. lim x3+8 46. lim 35. The following limits all have the indeterminate form 0/0. One of the x3 - 1 x- -2x-+ 6x + 8 limits does not exist, one is equal to 0, and one is a nonzero limit. Evalu- ate each limit algebraically if you can or investigate it numerically if you 47. lim . lim x - 27 -+27 x 1/3 - 3 cannot. In Exercises 49-56, evaluate in terms of the constant a. (a) lim *- + 3x + 2 x+ 2 (b) lim 101x - 2+x-1 49. lim (2a + x) 50. lim (4ah + 7a) 1+0 (c) lim 1-0 1 - ex 51. lim (41 - 2ar + 3a) 52. lim (x + a) - 4x2 36. The following limits all have the indeterminate form oo/co. One of x - a the limits does not exist. one is equal to 0, and one is a nonzero limit. Eval- uate each limit algebraically if you can or investigate it numerically if you 53. lim ~ Vx - Va lim Va + 2h - Ja cannot. x - a (a) lim 3 cot.x 1-04+x-1 (b) lim - 1-0 csc x 55. lim (x +a)' - al 56. lim (c) lim - 1-01+ 57. Evaluate lim With -1 Hint: Set x = $1 +h. express h as a In Exercises 37 and 38, a ball is launched straight up in the air and is acted function of x, and rewrite as a limit as x - 1. .h on by air resistance and gravity as in Example 7. The function H gives the maximum height that the ball attains as a function of the air-resistance 58. Evaluate lim With -1 Hint: Set x = 1 +h, express h as a parameter k. 4-0 With - 1 function of x, and rewrite as a limit as x -+ 1.96 CHAPTER 2 LIMITS Further Insights and Challenges In Exercises 59-62, find all values of c such that the limit exists. 63. For which sign, + or -, does the following limit exist? x2 - 5x - 6 (+ 3x + c 59. lim lim X -C x - 1 lim X ( x - 1 ) ) It cx - VI+ x2 61. lim 62. lim 2.6 The Squeeze Theorem and Trigonometric Limits y = u(x) In our study of the derivative, we will need to evaluate certain limits involving dental functions such as sine and cosine. The algebraic techniques of the previa y = f(x) are often ineffective for such functions, and other tools are required. In this ye discuss one such tool-the Squeeze Theorem-and use it to evaluate the trig y = 1(x) limits needed in Section 3.6. FIGURE 1 f is trapped between / and u. The Squeeze Theorem Consider a function f that is "trapped" between two functions /, for lower bound for upper bound, on an interval /. In other words, I(x)