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Name: ____________________ Period: ______ Date: ___________ AP Calc BC

Mr. Mellina

Chapter 5 Review: Logarithmic, Exponential,

and other Transcendental Functions

Topics:1. Derivative of Natural Log Functions 2. Derivative of Exponential & Log Functions, Logarithmic

Differentiation. 3. Integration with Logarithms 4. Integration of Exponential & Power Functions 5. Derivative of Inverse Functions 6. Derivative of Inverse Trig Functions 7. Integration with Inverse Trig functions.

HWSets

Topic1:Chapter5ReviewSetATopic2:Chapter5ReviewSetBTopic3:Chapter5ReviewSetCTopic4:Chapter5ReviewSetDTopic5:Chapter5ReviewSetETopic6:Chapter5ReviewSetFTopic7:Chapter5ReviewSetG

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Topic1:DerivativeofNaturalLogarithmicFunctions(Day1)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.

Inexercises9-16,findthederivativeofthefunction.9. ! " = ln 2" 10. ' " = ln 3") + 2" 11. ' " = " ln " 12. ' " = ln 2" +

3

13. , = ln -./0-.10 14. , = ln 0-

-12

15. , = 3

45 316- 16. , = 457-31-

InExercises17&18,findanequationofthetangentlinetothegraphofthefunctionatthegivenpoint.17. , = ln 2 + " + )

)/- , −1, 2 18. , = 2") + ln ") , 1, 2

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Topic2:DerivativeofExponential&LogarithmicFunctions,LogarithmicDifferentiation(Day2)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.Forexercises47-52,findthederivative.47. ! < = <)=> 48. ! " = ln ?@

3/?@49. , = =)- + =1)- 50. ℎ B = =1C

.)

51. ! " = -D

?.@ 52. , = 3=1+ >

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InExercises53&54,findanequationofthetangentlinetothegraphofthefunctionatthegivenpoint.53. ' " = =2-, (0, 1) 54. ℎ " = −"=)1-, (2, −2)InExercises55&56,findtheextremaandpointsofinflection(ifanyexist)ofthefunction.55. ' " = " + 1 =1-

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InExercises75-82,findthederivativeofthefunction.75. ' " = 3-13 76. ' " = 5+-77. ! < = )DI

>. 78. ' " = " 41+-

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79. ! " = log+ 1 − " 80. ℎ " = log7 --13

81. , = ")-/3 82. , = 3" + 5 -

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Topic3:IntegrationwithLogarithms(Day3)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.Inexercises21-26,findtheindefiniteintegral.21. 3

6-1) M" 22. -.

-D/3 M"23. NO5 -

3/PQN - M"

9

24. 45 -- M"

25. -.12-/3

-./3 M" 26. R-

- ) -/7

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Topic4:IntegrationofExponential&PowerFunctions(Day4)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.ForExercises57-60,83&84,findtheindefiniteintegral.57. "=31-.M" 58. ")=-D/3M"59. ?S@1?.@/3

?@ M" 60. ?.@1?T.@?.@/?T.@ M"

11

83. " + 1 5 -/3 .M" 84. )TU I>. M<

Forexercises61&63,85&86,evaluatethedefiniteintegral.61. "=1+-.M"3

V 63. ?@?@13 M"

+3

85. 6-M")

3 86. 9- )M"V10

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Topic5:DerivativeofInverseFunctions(Day5)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.

Inexercises39-42,verifythatfhasaninversefunction.Thenusethefunctionfandthegivenrealnumberatofind '13 ′ Z .39. ' " = "+ + 2,Z = −1 40. ' " = " " − 3,Z = 4 41. ' " = tan " , − ]

0 ≤ " ≤ ]0 ,Z =

++ 42. ' " = cos " , 0 ≤ " ≤ a,Z = 0

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Topic6:DerivativeofInverseTrigFunctions(Day6)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.Inexercises99-104,findthederivativeofthefunction.99. , = csc13 2") 100. , = 3

) tan13 =)-

101. , = " sec13 "

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102. , = ") − 4 − 2 sec13 -) , 2 < " < 4

103. , = " sin13 " ) − 2" + 2 1 − ") sin13 "

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Topic7:IntegrationwithInverseTrig(Day7)TheseproblemswereselectedfromtheReviewExercisesonpages400-402.

Inexercises105-110,findtheindefiniteintegral.105. 3

?.@/?T.@ M" 106. 3+/)7-. M"

107. -

31-S M" 108. 3- e-.10e M"

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109.fg5TU @

.0/-. M" 110. NO5TU()-)

310-. M"