Tag Archives: differentiation

Cover photo of Chapter 5 The Indeterminate Forms of the book Differential and Integral Calculus by Feliciano and Uy

Chapter 5: The Indeterminate Forms

5.1 Rolle’s Theorem

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5.2 Mean Value Theorem

Exercise 5.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

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5.3 L’Hospital’s Rule

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5.4 The Indeterminate Forms \displaystyle \frac{0}{0} and \displaystyle \frac{\infty }{\infty }

Exercise 5.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

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5.5 The Indeterminate Forms \displaystyle 0\left( \pm \infty \right) and \displaystyle \infty -\infty

Exercise 5.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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5.6 The Indeterminate Forms \displaystyle 0^0 , \displaystyle 1^\infty , and \displaystyle \infty ^0

Exercise 5.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

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Cover photo of Chapter 4 Differentiation of Transcendental Functions of the book Differential and Integral Calculus by Feliciano and Uy

Chapter 4: Differentiation of Transcendental Functions

4.1 The Function \displaystyle \frac{\sin u}{u}

Exercise 4.1

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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4.2 Differentiation of Trigonometric Functions

Exercise 4.2

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

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4.3 Differentiation of Inverse Trigonometric Functions

Exercise 4.3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

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4.4 The functions \displaystyle \left( 1+u \right)^{\frac{1}{u}}

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4.5 The Logarithmic and Exponential Functions

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4.6 Differentiation of Logarithmic Functions

Exercise 4.4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

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4.7 Logarithmic Differentiations

Exercise 4.5

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

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4.8 Differentiation of Exponential Functions

Exercise 4.6

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

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4.9 The Hyperbolic Functions

Exercise 4.7

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

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4.10 Differentiation of Hyperbolic Functions

Exercise 4.8

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

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4.11 Differentiation of Inverse Hyperbolic Functions

Exercise 4.9

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

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