FALL 2020 – Calculus Remaining Exam Assessment (Reply Key) 1. Think about the next one-sided restrict. → 18− ( 2 − 324 − 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 = ( ) to search out the boundaries: Step 1. Discover → −three − ( ). Reply: _______________ Step 2. Discover → 1 − ( ). Reply: ____________________ Step three. Discover → −1 − ( ). Reply: ____________________ Step four. Discover → −1 + ( ). Reply: ____________________ three. Use the graph to search out the indicated limits. Step 1. Discover → −1 − ( ). Reply: ____________________ Step 2. Discover → −1 + ( ). Reply: ____________________ Step three. Discover → −1 ( ). Reply: ____________________ four. Discover the restrict algebraically by factoring the expression first. → 2 ( four 2 − three − 10 − 2 ) Reply: ____________________ 5. Think about the graph of ( ). What’s the common fee of change of ( ) from 1 = four to 2 = 7? Please write your reply as an integer or simplified fraction. Reply: ____________________ 6. ( ) is the speed in meters per hour a snowmobile is touring at hours. Which of the next does the slope ′ ( ) symbolize? A) Route the snowmobile is touring at x hours. B) Common fee 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) Fee of change of the speed of the snowmobile at x hours. 7. Think about the perform ( ) = four three − 2 2 − + eight. Step 1. Interpret the that means of (1) = 9. A) The common fee of change from = zero to = 1 is 9. B) The slope of the tangent line at = 1 is 9. C) The slope of the secant line from (−1) to (1) is 9. D) The worth of the perform evaluated at = 1 is 9. Step 2. Interpret the that means of ′ (1) = 7. A) The slope of the curve at = 1 is 7. B) The common fee of change from = −1 to = 1 is 7. C) The peak of the perform at = 1 is 7. D) The common fee of change from = zero to = 1 is 7. eight. Discover the spinoff for the next perform. = − three 7 Reply: ____________________ 9. Discover the spinoff for ( ) = 5 2 + 2 three Reply: ____________________ 10. Discover the spinoff for ( ) = 5 three + three − 2 5 Reply: ____________________ 11. Use algebraic methods to rewrite ( ) = (three + 5)(three + four) as a sum or distinction; then discover ′ ( ). Reply: ____________________ 12. Use algebraic methods to rewrite ( ) = −three 6 + four three 2 as a sum or distinction; then discover ′ ( ). Reply: ____________________ 13. For the perform ( ) = −7 three − eight 2 − three , Step 1. Discover the slope of the tangent line at = −5. Reply: ____________________ Step 2. Discover the equation of the tangent line at = −5. Reply: ____________________ 14. A rock is falling. It’s ( ) = −16 2 + 410 toes off the bottom after seconds. Step 1. Discover the instantaneous fee of change of the rock’s place at = 2 seconds. Reply: ____________________ Step 2. When will the rock be 394 toes off the bottom? Reply: ____________________ 15. For the perform ( ) = 2 three + three 2 − 7 , discover the slope of the tangent line at = −three. Reply: =_______________ 16. Discover the restrict. → −9 − (5 2 + 6) Reply: ____________________ 17. Discover the restrict. → −2 − ( 18 − −19 + 2 ) Reply: ____________________ 18. Discover the restrict. → +∞ ( 15 11 2 + 10) Reply: ____________________ 19. Discover the restrict. → −∞ ( −5 2 − three 2 2 + 9 ) Reply: ____________________ 20. Discover the restrict. → −∞ ( three − 27 2 + three + 9 ) Reply: ____________________ 21. Discover the restrict. → −three + (−18 + 10 + three ) Reply: ____________________ 22. Discover the restrict. → −9 (√−10 + 14 + 16) Reply: ____________________ 23. Discover the restrict. → +∞ ( −three 2 + 16 + four 5 three + four 2 + 2 + 5 ) Reply: ____________________ 24. Think about the perform ( ) = { −four < 2 7 − 18 ≥ 2 . Step 1. Discover → 2 − ( ). Reply: ____________________ Step 2. Discover → 2 + ( ). Reply: ____________________ Step three. Discover → 2 ( ). Reply: ____________________ 25. Use the graph of = ( ) to reply the Question Assignment relating to the perform. Step 1. Discover → 1 − ( ). A) ____________ B) Does Not Exist Step 2. Discover → 1 + ( ). Reply: ____________________ Step three. Discover (1). Reply: ____________________ Step four. Is ( ) steady at = 1? A) Sure B) No 26. Use the graph of = ( ) to reply the Question Assignment relating to the perform. Step 1. Discover → −2 − ( ). A) ____________ B) Does Not Exist Step 2. Discover → −2 + ( ). Reply: ____________________ Step three. Discover (−2). Reply: ____________________ Step four. Is ( ) steady at = −2? A) Sure B) No 27. Think about the next perform: ( ) = { four 2 − 9 − three < −four 5 2 − 6 + 2 ≥ −four Step 1. At what -value is the perform discontinuous? Reply: ____________________ Step 2. What sort of discontinuity is on the discontinuous level? A) Non-Detachable Discontinuity B) Detachable Discontinuity C) Bounce Discontinuity 28. Use the Product Rule or Quotient Rule to search out the spinoff. ( ) = (− three − 7)(−2 −1 + 6) Reply: ′ ( ) =_______________ 29. Use the Product Rule or Quotient Rule to search out the spinoff. ( ) = eight three + 16 2 − 16 − 32 2 + four Reply: ′ ( ) =_______________ 30. Given (−6) = −2, ′ (−6) = −18, (−6) = −12, and ′ (−6) = 7, discover the worth of ℎ ′ (−6) based mostly on the perform beneath. ℎ( ) = ( ) ( ) Reply: ℎ ′ (−6) =_______________ 31. Use the Product Rule or Quotient Rule to search out the spinoff. ( ) = (three three + 9)(three four − 1) Reply: ′ ( ) =_______________ 32. Use the Product Rule or Quotient Rule to search out the spinoff. ( ) = three 6 − 2 four three − 5 Reply: ′ ( ) =_______________ 33. Discover the spinoff for the given perform. Write your reply utilizing optimistic and unfavorable exponents as a substitute of fractions and use fractional exponents as a substitute of radicals. ℎ( ) = (7 four + 9) three Reply: ____________________ 34. Discover the spinoff for the given perform. Write your reply utilizing optimistic and unfavorable exponents as a substitute of fractions and use fractional exponents as a substitute of radicals. ( ) = ( four + four −9 2 + 10) three Reply: ____________________ 35. Think about the perform. ( ) = − 2 + 6 − 6 Step 1. Discover all values of that correspond to horizontal tangent strains. Choose “None” if the perform doesn’t have any values of that correspond to horizontal tangent strains. Reply: ____________________ Step 2. Decide the open intervals on which the perform is rising and on which the perform is lowering. Enter ø to point the interval is empty. Reply: ____________________ 36. Think about the perform. ( ) = three three − 18 2 + 36 − 26 Step 1. Discover all values of that correspond to horizontal tangent strains. Choose “None” if the perform doesn’t have any values of that correspond to horizontal tangent strains. Reply: ____________________ Step 2. Decide the open intervals on which the perform is rising and on which the perform is lowering. Enter ø to point the interval is empty. Reply: ____________________ 37. Think about the perform. ( ) = + 7 − 1 Step 1. Discover all values of that correspond to horizontal tangent strains. Choose “None” if the perform doesn’t have any values of that correspond to horizontal tangent strains. Reply: ____________________ Step 2. Decide the open intervals on which the perform is rising and on which the perform is lowering. Enter ø to point the interval is empty. Reply: ____________________ 38. Think about the perform: ( ) = three(−three 2 + 48) 2 + four Step 1. Discover the essential values of the perform. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Take a look at to search out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 39. Think about the perform: ( ) = three − three 2 − 24 + four Step 1. Discover the essential values of the perform. Separate a number of solutions with commas. Reply: ____________________ Step 2. Use the First By-product Take a look at to search out any native extrema. Enter any native extrema as an ordered pair. Reply: ____________________ 40. Think about the perform ( ) = four three − 108 on the interval [−4, 4]. Discover absolutely the extrema for the perform on the given interval. Categorical your reply as an ordered pair ( , ( )). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 41. Think about the perform ( ) = four three − 12 2 − 288 on the interval [−7, 7]. Discover absolutely the extrema for the perform on the given interval. Categorical your reply as an ordered pair ( , ( )). Reply: Absolute Most: _______________ Absolute Minimal: _______________ 42. Think about the perform: ( ) = 7 three − eight 2 + 7 Step 1. Discover ′′( ). Reply: ____________________ Step 2. Consider ′′(−5), ′′(eight), and ′′(6), in the event that they exist. If they don’t exist, choose “Does Not Exist”. A) ″ (−5) =____________ B) ″ (−5) Does Not Exist A) ″ (eight) =____________ B) ″ (eight) Does Not Exist A) ″ (6) =____________ B) ″ (6) Does Not Exist 43. Think about the perform: ( ) = three 2 − 6√ four + eight Step 1. Discover ′′( ). Reply: ____________________ Step 2. Consider ′′(2), ′′(eight), and ′′(three), in the event that they exist. If they don’t exist, choose “Does Not Exist”. A) ″ (2) =____________ B) ″ (2) Does Not Exist A) ″ (eight) =____________ B) ″ (eight) Does Not Exist A) ″ (three) =____________ B) ″ (three) Does Not Exist 44. Think about the perform: ( ) = 5 three − 2 + 6 − 6 Discover ′′( ). Reply: ____________________ 45. Think about the perform: ( ) = −four three − 36 2 + 2 + 9 Step 1. Decide the intervals on which the perform 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 ( , )-pairs. A) Factors of Inflection: ____________ B) None 46. Think about the perform: ( ) = √5 + 1 Step 1. Discover ′′( ). Reply: ____________________ Step 2. Consider ′′(three), ′′(7), and ′′(6), in the event that they exist. If they don’t exist, choose “Does Not Exist”. A) ″ (three) =____________ B) ″ (three) Does Not Exist A) ″ (7) =____________ B) ″ (7) Does Not Exist A) ″ (6) =____________ B) ″ (6) Does Not Exist 47. Use the Second By-product Take a look at to search out all native extrema, if the check applies. In any other case, use the First By-product Take a look at. ( ) = 6 three + 81 2 + 360 A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 48. Think about the perform: ( ) = −four three + 6 2 + 240 − 12 Step 1. Discover the second spinoff of the given perform. Reply: ____________________ Step 2. Use the Second By-product Take a look at to find any native most or minimal factors within the graph of the given perform. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 49. Use the Second By-product Take a look at to search out all native extrema, if the check applies. In any other case, use the First By-product Take a look at. ( ) = 2 three + 6 2 − 48 + 18 A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 50. Think about the perform: ( ) = (2 2 + 11) 2 Step 1. Discover the second spinoff of the given perform. Reply: ____________________ Step 2. Use the Second By-product Take a look at to find any native most or minimal factors within the graph of the given perform. A) Native Maxima: ____________ B) No Native Maxima A) Native Minima: ____________ B) No Native Minima 51. Use the Second By-product Take a look at to search out all native extrema, if the check applies. In any other case, use the First By-product Take a look at. ( ) = four + 16 three − 7 A) Native maxima: No native maxima; Native minima: No native minima B) Native maxima: No native maxima; Native minima: (−12,zero) C) Native maxima: (−12, −6919); Native minima: No native minima D) Native maxima: No native maxima; Native minima: (−12, −6919) 52. Discover the next indefinite integral. ∫(−four 2 − 6) Reply: ____________________ 53. Discover the next indefinite integral. ∫( −2 + 5 − four 5 + eight ) Reply: ____________________ 54. Discover the next indefinite integral. ∫(−2 − eight −three + three 7 ) Reply: ____________________ 55. Carry out the indicated multiplication after which combine. ∫ three (2 − 9) Reply: ____________________ 56. Consider the particular integral beneath. three ∫ 1 −5 three Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 57. Consider the particular integral beneath. four ∫ three ( −6 2 − 6) Enter your reply in actual type or rounded to 2 decimal locations. Reply: ____________________ 58. Consider the particular integral beneath. 5 ∫ 1 (2 + four ) 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. ∫ ( 2 + 5 − 12) four 2 Reply: _______________ 60. Discover the next indefinite integral. ∫( − 5 6 ) Reply: ____________________ 61. Discover the next indefinite integral. ∫( 1 2 1 eight + 7) Reply: ____________________ 62. Discover the next indefinite integral. ∫(12 + three ) Reply: ____________________ 63. Discover the next indefinite integral. ∫(5 9 − 6 + 1 5 ) Reply: ____________________ 64. Simplify the indicated quotient after which combine. ∫ −5 6 + 5 − eight 6 Reply: ____________________ 65. Think about the perform: ( ) = −2 three − 5 2 − 9 + four Step 1. Discover ′′( ). Reply: ____________________ Step 2. Consider ′′(four), ′′(−9), and ′′(zero), in the event that they exist. If they don’t exist, choose “Does Not Exist”. A) ″ (four) =____________ B) ″ (four) Does Not Exist A) ″ (−9) =____________ B) ″ (−9) Does Not Exist A) ″ (zero) =____________ B) ″ (zero) Does Not Exist 66. Think about the perform: ( ) = 2 + 5 −6 − eight Step 1. Discover ′′( ). Reply: ____________________ Step 2. Consider ′′(10), ′′(7), and ′′(−three), in the event that they exist. If they don’t exist, choose “Does Not Exist”. A) ″ (10) =____________ B) ″ (10) Does Not Exist A) ″ (7) =____________ B) ″ (7) Does Not Exist A) ″ (−three) =____________ B) ″ (−three) Does Not Exist 67. Think about the perform: ( ) = 5 2 − √ + 6 Discover ′′( ). Reply: ____________________ 68. Think about the perform: ( ) = 9 2 + eight − 10 Step 1. Decide the intervals on which the perform 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 ( , )-pairs. A) Factors of Inflection: ____________ B) None 69. Think about the perform: ( ) = three + 72√ − 5 Step 1. Decide the intervals on which the perform 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 ( , )-pairs. A) Factors of Inflection: ____________ B) None 1. Step 1.Right Reply: 35, 35.9, 35.99, 35.999 Step 2.Right Reply: 36 2. Step 1.Right Reply: → −three − ( ) = −1 Step 2.Right Reply: → 1 − ( ) = −1 Step three.Right Reply: → −1 − ( ) = eight Step four.Right Reply: → −1 + ( ) = −2 three. Step 1.Right Reply: −four Step 2.Right Reply: 1 Step three.Right Reply: Does Not Exist four. Right Reply: 13 5. Right Reply: 2 three 6. Right Reply: Fee of change of the speed of the snowmobile at hours. 7. Step 1.Right Reply: The worth of the perform evaluated at = 1 is 9. Step 2.Right Reply: The slope of the curve at = 1 is 7. eight. Right Reply: ′ = − three 7 − four 7 9. Right Reply: ′ ( ) = 10 + 6 2 10. Right Reply: ′ ( ) = 15 2 − 10 four 11. Right Reply: ′ ( ) = 18 + 27 12. Right Reply: ′ ( ) = −12 three + four 13. Step 1.Right Reply: The slope of the tangent line at = −5 is −448. Step 2.Right Reply: = −448 − 1550 14. Step 1.Right Reply: −64 Step 2.Right Reply: 1 15. Right Reply: = 29 16. Right Reply: 411 17. Right Reply: 1 2 18. Right Reply: zero 19. Right Reply: −5 2 20. Right Reply: −∞ 21. Right Reply: +∞ 22. Right Reply: √104 + 16 23. Right Reply: zero 24. Step 1.Right Reply: −four Step 2.Right Reply: −four Step three.Right Reply: −four 25. Step 1.Right Reply: three Step 2.Right Reply: 2 Step three.Right Reply: three Step four.Right Reply: No 26. Step 1.Right Reply: −three Step 2.Right Reply: −three Step three.Right Reply: 1 Step four.Right Reply: No 27. Step 1.Right Reply: −four Step 2.Right Reply: Bounce Discontinuity 28. Right Reply: ′ ( ) = −18 2 + four − 14 −2 29. Right Reply: ′ ( ) = eight 30. Right Reply: ℎ ′ (−6) = 115 72 31. Right Reply: ′ ( ) = 63 6 + 108 three − 9 2 32. Right Reply: ′ ( ) = 36 eight − 90 5 + 24 2 (four three − 5) 2 33. Right Reply: three(7 four + 9) 2 (28 three ) 34. Right Reply: three ( four + four −9 2 + 10) 2 ( (−9 2 + 10)(four three) −( four + four)(−18 ) (−9 2 + 10)2 ) 35. Step 1.Right Reply: three Step 2.Right Reply: Rising: (−∞, three), Reducing: (three, ∞) 36. Step 1.Right Reply: 2 Step 2.Right Reply: Rising: (−∞, ∞), Reducing: ø 37. Step 1.Right Reply: None Step 2.Right Reply: Rising: ø, Reducing: (−∞, 1), (1, ∞) 38. Step 1.Right Reply: = −four, zero, four Step 2.Right Reply: Native Maxima: (zero, 6916), Native Minima: (−four, four), (four, four) 39. Step 1.Right Reply: = −2, four Step 2.Right Reply: Native Maxima: (−2, 32), Native Minima: (four, −76) 40. Right Reply: Absolute Most: (−three, 216) Absolute Minimal: (three, −216) 41. Right Reply: Absolute Most: (−four, 704) Absolute Minimal: (6, −1296) 42. Step 1.Right Reply: ′′( ) = 42 − 16 Step 2.Right Reply: ′′(−5) = −226, ′′(eight) = 320, ′′(6) = 236 43. Step 1.Right Reply: ′′( ) = 6 + 9 eight −7 four Step 2.Right Reply: ′′(2) = 6 + 9 √2 four 32 , ′′(eight) = 6 + 9 √eight four 512 , ′′(three) = 6 + √three four eight 44. Right Reply: ′′( ) = 30 − 2 45. Step 1.Right Reply: Concave Up: (−∞, −three), Concave Down: (−three, ∞) Step 2.Right Reply: Factors of Inflection: (−three, −213) 46. Step 1.Right Reply: ′′( ) = − 25 four (5 + 1) −three 2 Step 2.Right Reply: ′′(three) = −25 256, ′′(7) = −25 864, ′′(6) = − 25√31 3844 47. Right Reply: Native Maxima: (−5, −525), Native Minima: (−four, −528) 48. Step 1.Right Reply: ′′( ) = −24 + 12 Step 2.Right Reply: Native Maxima: (5, 838), Native Minima: (−four, −620) 49. Right Reply: Native Maxima: (−four, 178), Native Minima: (2, −38) 50. Step 1.Right Reply: ′′( ) = 48 2 + 88 Step 2.Right Reply: Native Maxima: No Native Maxima, Native Minima: (zero, 121) 51. Right Reply: Native maxima: No native maxima; Native minima: (−12, −6919) 52. Right Reply: − four three three − 6 + 53. Right Reply: −2 ln( ⃒ ⃒ ) + 25 1 5 + eight + 54. Right Reply: −2 + four −2 + three 7 + 55. Right Reply: 2 5 5 − 9 four four + 56. Right Reply: −20 9 57. Right Reply: −13 2 58. Right Reply: eight + four 5 − four ≈ 590.78 59. Right Reply: 74 three 60. Right Reply: − 5 6 + 61. Right Reply: four 9 9 eight + 7 + 62. Right Reply: 12 + three 2 2 + 63. Right Reply: 1 2 10 − 6 ln( ⃒ ⃒ ) − 1 four −four + 64. Right Reply: −5 + ln( ⃒ ⃒ ) + eight 5 −5 + 65. Step 1.Right Reply: ′′( ) = −12 − 10 Step 2.Right Reply: ′′(four) = −58, ′′(−9) = 98, ′′(zero) = −10 66. Step 1.Right Reply: ′′( ) = 168(−6 − eight) −three Step 2.Right Reply: ′′(10) = −21 39304, ′′(7) = −21 15625, ′′(−three) = 21 125 67. Right Reply: ′′( ) = 10 + 1 four −three 2 68. Step 1.Right Reply: Concave Up: (−∞, ∞), Concave Down: None Step 2.Right Reply: Factors of Inflection: None 69. Step 1.Right Reply: Concave Up: (√9 5 , ∞), Concave Down: (zero, √9 5 ) Step 2.Right Reply: Factors of Inflection: (√9 5 , −5 + 75√three 5 )

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