FALL 2020 - Calculus Remaining Examination Evaluation (Reply Key) 1. Take into account the next one-sided restrict. πππ π₯ β 18β ( π₯ 2 β 324 π₯ β 18 ) Step 1. Approximate the restrict by filling within the desk. Spherical to the closest thousandth. Step 2. Decide the worth of the one-sided restrict. Reply: ____________________ 2. Use the graph of π¦ = π (π₯) to seek out the bounds: Step 1. Discover πππ π₯ β βthree β π (π₯). Reply: _______________ Step 2. Discover πππ π₯ β 1 β π (π₯). Reply: ____________________ Step three. Discover πππ π₯ β β1 β π (π₯). Reply: ____________________ Step four. Discover πππ π₯ β β1 + π (π₯). Reply: ____________________ three. Use the graph to seek out the indicated limits. Step 1. Discover πππ π₯ β β1 β π (π₯). Reply: ____________________ Step 2. Discover πππ π₯ β β1 + π (π₯). Reply: ____________________ Step three. Discover πππ π₯ β β1 π (π₯). Reply: ____________________ four. Discover the restrict algebraically by factoring the expression first. πππ π₯ β 2 ( 4π₯ 2 β 3π₯ β 10 π₯ β 2 ) Reply: ____________________ 5. Take into account the graph of π (π₯). What's the common charge of change of π (π₯) from π₯1 = four to π₯2 = 7? Please write your reply as an integer or simplified fraction. Reply: ____________________ 6. π(π₯) is the rate in meters per hour a snowmobile is touring at π₯ hours. Which of the next does the slope π β² (π₯) symbolize? A) Route the snowmobile is touring at x hours. B) Common charge of change within the velocity of the snowmobile in meters per hour at x hours. C) Distance in meters the snowmobile has traveled in x hours. D) Charge of change of the rate of the snowmobile at x hours. 7. Take into account the operate π(π₯) = 4π₯ three β 2π₯ 2 β π₯ + eight. Step 1. Interpret the which means of π(1) = 9. A) The typical charge of change from π₯ = zero to π₯ = 1 is 9. B) The slope of the tangent line at π₯ = 1 is 9. C) The slope of the secant line from π(β1) to π(1) is 9. D) The worth of the operate evaluated at π₯ = 1 is 9. Step 2. Interpret the which means of π β² (1) = 7. A) The slope of the curve at π₯ = 1 is 7. B) The typical charge of change from π₯ = β1 to π₯ = 1 is 7. C) The peak of the operate at π₯ = 1 is 7. D) The typical charge of change from π₯ = zero to π₯ = 1 is 7. eight. Discover the by-product for the next operate. π¦ = βπ₯ three 7 Reply: ____________________ 9. Discover the by-product for π(π₯) = 5π₯ 2 + 2π₯ three Reply: ____________________ 10. Discover the by-product for π (π₯) = 5π₯ three + three β 2π₯ 5 Reply: ____________________ 11. Use algebraic methods to rewrite π(π₯) = (3π₯ + 5)(3π₯ + four) as a sum or distinction; then discover π β² (π₯). Reply: ____________________ 12. Use algebraic methods to rewrite π(π₯) = β3π₯ 6 + 4π₯ three π₯2 as a sum or distinction; then discover π β² (π₯). Reply: ____________________ 13. For the operate π (π₯) = β7π₯ three β 8π₯ 2 β 3π₯, Step 1. Discover the slope of the tangent line at π₯ = β5. Reply: ____________________ Step 2. Discover the equation of the tangent line at π₯ = β5. Reply: ____________________ 14. A rock is falling. It's π (π₯) = β16π₯ 2 + 410 toes off the bottom after π₯ seconds. Step 1. Discover the instantaneous charge of change of the rock's place at π₯ = 2 seconds. Reply: ____________________ Step 2. When will the rock be 394 toes off the bottom? Reply: ____________________ 15. For the operate π(π₯) = 2π₯ three + 3π₯ 2 β 7π₯, discover the slope of the tangent line at π₯ = βthree. Reply: π =_______________ 16. Discover the restrict. πππ π₯ β β9 β (5π₯ 2 + 6) Reply: ____________________ 17. Discover the restrict. πππ π₯ β β2 β ( 18 β π₯ β19π₯ + 2 ) Reply: ____________________ 18. Discover the restrict. πππ π₯ β +β ( 15π₯ 11π₯2 + 10) Reply: ____________________ 19. Discover the restrict. πππ π₯ β ββ ( β5π₯ 2 β three 2π₯2 + 9 ) Reply: ____________________ 20. Discover the restrict. πππ π₯ β ββ ( π₯ three β 27 π₯2 + 3π₯ + 9 ) Reply: ____________________ 21. Discover the restrict. πππ π₯ β βthree + (β18π₯ + 10 π₯ + three ) Reply: ____________________ 22. Discover the restrict. πππ π₯ β β9 (ββ10π₯ + 14 + 16) Reply: ____________________ 23. Discover the restrict. πππ π₯ β +β ( β3π₯ 2 + 16π₯ + four 5π₯3 + 4π₯2 + 2π₯ + 5 ) Reply: ____________________ 24. Take into account the operate π (π₯) = { βfour πππ₯ < 2 7π₯ β 18 πππ₯ β₯ 2 . Step 1. Discover πππ π₯ β 2 β π (π₯). Reply: ____________________ Step 2. Discover πππ π₯ β 2 + π (π₯). Reply: ____________________ Step three. Discover πππ π₯ β 2 π (π₯). Reply: ____________________ 25. Use the graph of π¦ = π (π₯) to reply the query concerning the operate. Step 1. Discover πππ π₯ β 1 β π (π₯). A) ____________ B) Does Not Exist Step 2. Discover πππ π₯ β 1 + π (π₯). Reply: ____________________ Step three. Discover π (1). Reply: ____________________ Step four. Is π (π₯) steady at π₯ = 1? A) Sure B) No 26. Use the graph of π¦ = π (π₯) to reply the query concerning the operate. Step 1. Discover πππ π₯ β β2 β π (π₯). A) ____________ B) Does Not Exist Step 2. Discover πππ π₯ β β2 + π (π₯). Reply: ____________________ Step three. Discover π (β2). Reply: ____________________ Step four. Is π (π₯) steady at π₯ = β2? A) Sure B) No 27. Take into account the next operate: π (π₯) = { 4π₯ 2 β 9π₯ β three πππ₯ < βfour 5π₯ 2 β 6π₯ + 2 πππ₯ β₯ βfour Step 1. At what π₯-value is the operate discontinuous? Reply: ____________________ Step 2. What kind of discontinuity is on the discontinuous level? A) Non-Detachable Discontinuity B) Detachable Discontinuity C) Soar Discontinuity 28. Use the Product Rule or Quotient Rule to seek out the by-product. π(π₯) = (βπ₯ three β 7)(β2π₯ β1 + 6) Reply: π β² (π₯) =_______________ 29. Use the Product Rule or Quotient Rule to seek out the by-product. π(π₯) = 8π₯ three + 16π₯ 2 β 16π₯ β 32 2π₯ + four Reply: π β² (π₯) =_______________ 30. Given π(β6) = β2, π β² (β6) = β18, π(β6) = β12, and π β² (β6) = 7, discover the worth of β β² (β6) primarily based on the operate beneath. β(π₯) = π(π₯) π (π₯) Reply: β β² (β6) =_______________ 31. Use the Product Rule or Quotient Rule to seek out the by-product. π(π₯) = (3π₯ three + 9)(3π₯ four β 1) Reply: π β² (π₯) =_______________ 32. Use the Product Rule or Quotient Rule to seek out the by-product. π(π₯) = 3π₯ 6 β 2 4π₯3 β 5 Reply: π β² (π₯) =_______________ 33. Discover the by-product for the given operate. Write your reply utilizing optimistic and destructive exponents as an alternative of fractions and use fractional exponents as an alternative of radicals. β(π₯) = (7π₯ four + 9) three Reply: ____________________ 34. Discover the by-product for the given operate. Write your reply utilizing optimistic and destructive exponents as an alternative of fractions and use fractional exponents as an alternative of radicals. π (π₯) = ( π₯ four + four β9π₯2 + 10) three Reply: ____________________ 35. Take into account the operate. π (π₯) = βπ₯ 2 + 6π₯ β 6 Step 1. Discover all values of π₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 36. Take into account the operate. π (π₯) = 3π₯ three β 18π₯ 2 + 36π₯ β 26 Step 1. Discover all values of π₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 37. Take into account the operate. π (π₯) = π₯ + 7 π₯ β 1 Step 1. Discover all values of π₯ that correspond to horizontal tangent traces. Choose "None" if the operate doesn't have any values of π₯ that correspond to horizontal tangent traces. Reply: ____________________ Step 2. Decide the open intervals on which the operate is rising and on which the operate is reducing. Enter ΓΈ to point the interval is empty. Reply: ____________________ 38. Take into account the operate: π (π₯) = three(β3π₯ 2 + 48) 2 + four Step 1. Discover the important values of the operate. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Check to seek out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 39. Take into account the operate: π (π₯) = π₯ three β 3π₯ 2 β 24π₯ + four Step 1. Discover the important values of the operate. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Check to seek out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 40. Take into account the operate π (π₯) = 4π₯ three β 108π₯ on the interval [β4, 4]. Discover absolutely the extrema for the operate on the given interval. Specific your reply as an ordered pair (π₯, π (π₯)). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 41. Take into account the operate π (π₯) = 4π₯ three β 12π₯ 2 β 288π₯ on the interval [β7, 7]. Discover absolutely the extrema for the operate on the given interval. Specific your reply as an ordered pair (π₯, π (π₯)). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 42. Take into account the operate: π (π₯) = 7π₯ three β 8π₯ 2 + 7π₯ Step 1. Discover π β²β²(π₯). Reply: ____________________ Step 2. Consider π β²β²(β5), π β²β²(eight), and π β²β²(6), in the event that they exist. If they don't exist, choose "Does Not Exist". A) π β³ (β5) =____________ B) π β³ (β5) Does Not Exist A) π β³ (eight) =____________ B) π β³ (eight) Does Not Exist A) π β³ (6) =____________ B) π β³ (6) Does Not Exist 43. Take into account the operate: π (π₯) = 3π₯ 2 β 6βπ₯ four + eight Step 1. Discover π β²β²(π₯). Reply: ____________________ Step 2. Consider π β²β²(2), π β²β²(eight), and π β²β²(three), in the event that they exist. If they don't exist, choose "Does Not Exist". A) π β³ (2) =____________ B) π β³ (2) Does Not Exist A) π β³ (eight) =____________ B) π β³ (eight) Does Not Exist A) π β³ (three) =____________ B) π β³ (three) Does Not Exist 44. Take into account the operate: π (π₯) = 5π₯ three β π₯ 2 + 6π₯ β 6 Discover π β²β²(π₯). Reply: ____________________ 45. Take into account the operate: π (π₯) = β4π₯ three β 36π₯ 2 + 2π₯ + 9 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π₯, π¦)-pairs. A) Factors of Inflection: ____________ B) None 46. Take into account the operate: π (π₯) = β5π₯ + 1 Step 1. Discover π β²β²(π₯). Reply: ____________________ Step 2. Consider π β²β²(three), π β²β²(7), and π β²β²(6), in the event that they exist. If they don't exist, choose "Does Not Exist". A) π β³ (three) =____________ B) π β³ (three) Does Not Exist A) π β³ (7) =____________ B) π β³ (7) Does Not Exist A) π β³ (6) =____________ B) π β³ (6) Does Not Exist 47. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. π (π₯) = 6π₯ three + 81π₯ 2 + 360π₯ A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 48. Take into account the operate: π (π₯) = β4π₯ three + 6π₯ 2 + 240π₯ β 12 Step 1. Discover the second by-product of the given operate. Reply: ____________________ Step 2. Use the Second By-product Check to find any native most or minimal factors within the graph of the given operate. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 49. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. π (π₯) = 2π₯ three + 6π₯ 2 β 48π₯ + 18 A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 50. Take into account the operate: π (π₯) = (2π₯ 2 + 11) 2 Step 1. Discover the second by-product of the given operate. Reply: ____________________ Step 2. Use the Second By-product Check to find any native most or minimal factors within the graph of the given operate. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 51. Use the Second By-product Check to seek out all native extrema, if the take a look at applies. In any other case, use the First By-product Check. π(π₯) = π₯ four + 16π₯ three β 7 A) Native maxima: No native maxima; Native minima: No native minima B) Native maxima: No native maxima; Native minima: (β12,zero) C) Native maxima: (β12, β6919); Native minima: No native minima D) Native maxima: No native maxima; Native minima: (β12, β6919) 52. Discover the next indefinite integral. β«(β4π₯ 2 β 6)ππ₯ Reply: ____________________ 53. Discover the next indefinite integral. β«( β2 π₯ + 5π₯ β four 5 + 8π π₯ )ππ₯ Reply: ____________________ 54. Discover the next indefinite integral. β«(β2π π₯ β 8π₯ βthree + three 7 )ππ₯ Reply: ____________________ 55. Carry out the indicated multiplication after which combine. β«π₯ three (2π₯ β 9)ππ₯ Reply: ____________________ 56. Consider the particular integral beneath. three β« 1 β5 π₯3ππ₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 57. Consider the particular integral beneath. four β« three ( β6 π₯2 β 6)ππ₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 58. Consider the particular integral beneath. 5 β« 1 (2 + 4π π₯ )ππ₯ Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 59. Consider the next particular integral. Write the precise reply. Don't spherical. β« (π₯ 2 + 5π₯ β 12)ππ₯ four 2 Reply: _______________ 60. Discover the next indefinite integral. β«(π π₯ β 5 6 )ππ₯ Reply: ____________________ 61. Discover the next indefinite integral. β«( 1 2 π₯ 1 eight + 7)ππ₯ Reply: ____________________ 62. Discover the next indefinite integral. β«(12π π‘ + 3π‘)ππ‘ Reply: ____________________ 63. Discover the next indefinite integral. β«(5π₯ 9 β 6 π₯ + 1 π₯5 )ππ₯ Reply: ____________________ 64. Simplify the indicated quotient after which combine. β« β5π₯ 6 + π₯ 5 β eight π₯6 ππ₯ Reply: ____________________ 65. Take into account the operate: π (π₯) = β2π₯ three β 5π₯ 2 β 9π₯ + four Step 1. Discover π β²β²(π₯). Reply: ____________________ Step 2. Consider π β²β²(four), π β²β²(β9), and π β²β²(zero), in the event that they exist. If they don't exist, choose "Does Not Exist". A) π β³ (four) =____________ B) π β³ (four) Does Not Exist A) π β³ (β9) =____________ B) π β³ (β9) Does Not Exist A) π β³ (zero) =____________ B) π β³ (zero) Does Not Exist 66. Take into account the operate: π (π₯) = 2π₯ + 5 β6π₯ β eight Step 1. Discover π β²β²(π₯). Reply: ____________________ Step 2. Consider π β²β²(10), π β²β²(7), and π β²β²(βthree), in the event that they exist. If they don't exist, choose "Does Not Exist". A) π β³ (10) =____________ B) π β³ (10) Does Not Exist A) π β³ (7) =____________ B) π β³ (7) Does Not Exist A) π β³ (βthree) =____________ B) π β³ (βthree) Does Not Exist 67. Take into account the operate: π (π₯) = 5π₯ 2 β βπ₯ + 6 Discover π β²β²(π₯). Reply: ____________________ 68. Take into account the operate: π (π₯) = 9π₯ 2 + 8π₯ β 10 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π₯, π¦)-pairs. A) Factors of Inflection: ____________ B) None 69. Take into account the operate: π (π₯) = π₯ three + 72βπ₯ β 5 Step 1. Decide the intervals on which the operate is concave upwards or concave downwards. A) Concave Up: ____________ B) By no means Concave Up A) Concave Down: ____________ B) By no means Concave Down Step 2. Find any factors of inflection. Enter your reply as (π₯, π¦)-pairs. A) Factors of Inflection: ____________ B) None 1. Step 1.Appropriate Reply: 35, 35.9, 35.99, 35.999 Step 2.Appropriate Reply: 36 2. Step 1.Appropriate Reply: πππ π₯ β βthree β π (π₯) = β1 Step 2.Appropriate Reply: πππ π₯ β 1 β π (π₯) = β1 Step three.Appropriate Reply: πππ π₯ β β1 β π (π₯) = eight Step four.Appropriate Reply: πππ π₯ β β1 + π (π₯) = β2 three. Step 1.Appropriate Reply: βfour Step 2.Appropriate Reply: 1 Step three.Appropriate Reply: Does Not Exist four. Appropriate Reply: 13 5. Appropriate Reply: 2 three 6. Appropriate Reply: Charge of change of the rate of the snowmobile at π₯ hours. 7. Step 1.Appropriate Reply: The worth of the operate evaluated at π₯ = 1 is 9. Step 2.Appropriate Reply: The slope of the curve at π₯ = 1 is 7. eight. Appropriate Reply: π¦ β² = β three 7 π₯ β four 7 9. Appropriate Reply: π β² (π₯) = 10π₯ + 6π₯ 2 10. Appropriate Reply: π β² (π₯) = 15π₯ 2 β 10π₯ four 11. Appropriate Reply: π β² (π₯) = 18π₯ + 27 12. Appropriate Reply: π β² (π₯) = β12π₯ three + four 13. Step 1.Appropriate Reply: The slope of the tangent line at π₯ = β5 is β448. Step 2.Appropriate Reply: π¦ = β448π₯ β 1550 14. Step 1.Appropriate Reply: β64 Step 2.Appropriate Reply: 1 15. Appropriate Reply: π = 29 16. Appropriate Reply: 411 17. Appropriate Reply: 1 2 18. Appropriate Reply: zero 19. Appropriate Reply: β5 2 20. Appropriate Reply: ββ 21. Appropriate Reply: +β 22. Appropriate Reply: β104 + 16 23. Appropriate Reply: zero 24. Step 1.Appropriate Reply: βfour Step 2.Appropriate Reply: βfour Step three.Appropriate Reply: βfour 25. Step 1.Appropriate Reply: three Step 2.Appropriate Reply: 2 Step three.Appropriate Reply: three Step four.Appropriate Reply: No 26. Step 1.Appropriate Reply: βthree Step 2.Appropriate Reply: βthree Step three.Appropriate Reply: 1 Step four.Appropriate Reply: No 27. Step 1.Appropriate Reply: βfour Step 2.Appropriate Reply: Soar Discontinuity 28. Appropriate Reply: π β² (π₯) = β18π₯ 2 + 4π₯ β 14π₯ β2 29. Appropriate Reply: π β² (π₯) = 8π₯ 30. Appropriate Reply: β β² (β6) = 115 72 31. Appropriate Reply: π β² (π₯) = 63π₯ 6 + 108π₯ three β 9π₯ 2 32. Appropriate Reply: π β² (π₯) = 36π₯ eight β 90π₯ 5 + 24π₯ 2 (4π₯3 β 5) 2 33. Appropriate Reply: three(7π₯ four + 9) 2 (28π₯ three ) 34. Appropriate Reply: three ( π₯ four + four β9π₯ 2 + 10) 2 ( (β9π₯ 2 + 10)(4π₯ three) β(π₯ four + four)(β18π₯) (β9π₯ 2 + 10)2 ) 35. Step 1.Appropriate Reply: three Step 2.Appropriate Reply: Rising: (ββ, three), Lowering: (three, β) 36. Step 1.Appropriate Reply: 2 Step 2.Appropriate Reply: Rising: (ββ, β), Lowering: ΓΈ 37. Step 1.Appropriate Reply: None Step 2.Appropriate Reply: Rising: ΓΈ, Lowering: (ββ, 1), (1, β) 38. Step 1.Appropriate Reply: π₯ = βfour, zero, four Step 2.Appropriate Reply: Native Maxima: (zero, 6916), Native Minima: (βfour, four), (four, four) 39. Step 1.Appropriate Reply: π₯ = β2, four Step 2.Appropriate Reply: Native Maxima: (β2, 32), Native Minima: (four, β76) 40. Appropriate Reply: Absolute Most: (βthree, 216) Absolute Minimal: (three, β216) 41. Appropriate Reply: Absolute Most: (βfour, 704) Absolute Minimal: (6, β1296) 42. Step 1.Appropriate Reply: π β²β²(π₯) = 42π₯ β 16 Step 2.Appropriate Reply: π β²β²(β5) = β226, π β²β²(eight) = 320, π β²β²(6) = 236 43. Step 1.Appropriate Reply: π β²β²(π₯) = 6 + 9 eight π₯ β7 four Step 2.Appropriate Reply: π β²β²(2) = 6 + 9 β2 four 32 , π β²β²(eight) = 6 + 9 βeight four 512 , π β²β²(three) = 6 + βthree four eight 44. Appropriate Reply: π β²β²(π₯) = 30π₯ β 2 45. Step 1.Appropriate Reply: Concave Up: (ββ, βthree), Concave Down: (βthree, β) Step 2.Appropriate Reply: Factors of Inflection: (βthree, β213) 46. Step 1.Appropriate Reply: π β²β²(π₯) = β 25 four (5π₯ + 1) βthree 2 Step 2.Appropriate Reply: π β²β²(three) = β25 256, π β²β²(7) = β25 864, π β²β²(6) = β 25β31 3844 47. Appropriate Reply: Native Maxima: (β5, β525), Native Minima: (βfour, β528) 48. Step 1.Appropriate Reply: π β²β²(π₯) = β24π₯ + 12 Step 2.Appropriate Reply: Native Maxima: (5, 838), Native Minima: (βfour, β620) 49. Appropriate Reply: Native Maxima: (βfour, 178), Native Minima: (2, β38) 50. Step 1.Appropriate Reply: π β²β²(π₯) = 48π₯ 2 + 88 Step 2.Appropriate Reply: Native Maxima: No Native Maxima, Native Minima: (zero, 121) 51. Appropriate Reply: Native maxima: No native maxima; Native minima: (β12, β6919) 52. Appropriate Reply: β four three π₯ three β 6π₯ + πΆ 53. Appropriate Reply: β2 ln( β π₯β ) + 25π₯ 1 5 + 8π π₯ + πΆ 54. Appropriate Reply: β2π π₯ + 4π₯ β2 + three 7 π₯ + πΆ 55. Appropriate Reply: 2 5 π₯ 5 β 9 four π₯ four + πΆ 56. Appropriate Reply: β20 9 57. Appropriate Reply: β13 2 58. Appropriate Reply: eight + 4π 5 β 4π β 590.78 59. Appropriate Reply: 74 three 60. Appropriate Reply: π π₯ β 5 6 π₯ + πΆ 61. Appropriate Reply: four 9 π₯ 9 eight + 7π₯ + πΆ 62. Appropriate Reply: 12π π‘ + three 2 π‘ 2 + πΆ 63. Appropriate Reply: 1 2 π₯ 10 β 6 ln( β π₯β ) β 1 four π₯ βfour + πΆ 64. Appropriate Reply: β5π₯ + ln( β π₯β ) + eight 5 π₯ β5 + πΆ 65. Step 1.Appropriate Reply: π β²β²(π₯) = β12π₯ β 10 Step 2.Appropriate Reply: π β²β²(four) = β58, π β²β²(β9) = 98, π β²β²(zero) = β10 66. Step 1.Appropriate Reply: π β²β²(π₯) = 168(β6π₯ β eight) βthree Step 2.Appropriate Reply: π β²β²(10) = β21 39304, π β²β²(7) = β21 15625, π β²β²(βthree) = 21 125 67. Appropriate Reply: π β²β²(π₯) = 10 + 1 four π₯ βthree 2 68. Step 1.Appropriate Reply: Concave Up: (ββ, β), Concave Down: None Step 2.Appropriate Reply: Factors of Inflection: None 69. Step 1.Appropriate Reply: Concave Up: (β9 5 , β), Concave Down: (zero, β9 5 ) Step 2.Appropriate Reply: Factors of Inflection: (β9 5 , β5 + 75βthree 5 )

Why Work with Us

Top Quality and Well-Researched Papers

. Our system allows you to choose your academic level: high school, college/university or professional, and we will assign a writer who has a right qualification.

Professional and Experienced Academic Writers

We have a wide team of professional writers with experience in academic and formal business writing.

Free Unlimited Revisions

Ordering custom papers from us is customer friendly. You can do this yourself after logging into your personal account or by contacting our support through chat or via email.

Prompt Delivery and 100% Money-Back-Guarantee

We are familiar with various schools deadlines. As such, all papers are delivered on time to allow you time to review before submitting it. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We have mordernized our writing in accordance with current technologies. Our editors carefully review all quotations and references in the text. We also promise maximum privacy and confidentiality in all of our services.

24/7 Customer Support

Our professional support agents are available 24 - 7 days a week and committed to providing you with the best customer experience by answering all your queries.

Try it now!

How it works?

Follow these steps to get your essay paper done

Place your order

Fill all the order form sections by providing details of your assignment.

Proceed with the payment

Choose the payment model that suits you most.

Receive the final file of the done paper

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper when deadlines are closing at very late hours of the night. Sleep tight, we will cover your back. You can order any assignment.

Essays

We work on all models of college papers within the set deadlines. We take care of all your paper needs and give a 24/7 customer care support system.

Admissions

Admission Essays & Business Writing Help

An admission essay is an application essay. You can rest assurred that through our service we will write the best admission essay for you.

Reviews

Editing Support

We format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.

Reviews

Revision Support

If you think your paper could be improved, you can request a review.. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.