Deck 2: Limits and Derivatives

Question 1

Answer 1

Question 2

Differentiate.

Answer 2

Question 3

Answer 3

Question 4

The position function of a particle is given by

Question 5

Question 6

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Question 9

Find an equation of the tangent line to the given curve at the indicated point.

Question 10

Question 11

Question 12

Find the derivative of the function.

Question 13

Find the derivative of the function.

Question 14

Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of
intersection of the curves.Show that the curves of the given equations are orthogonal.

Question 15

Question 16

Differentiate.

Question 17

Question 18

Question 19

Question 20

Question 21

Find the differential of the function at the indicated number.

Question 22

Question 23

Question 24

Question 25

Question 26

Question 27

Question 28

Find the derivative of the function.

Question 29

Question 30

Question 31

Find the differential of the function at the indicated number.

Question 32

Question 33

Question 34

Question 35

Two chemicals react to form another chemical.Suppose that the amount of chemical formed in
time t (in hours) is given by

Question 36

Question 37

Find an equation of the tangent line to the curve

Question 38

Question 39

Two curves are said to be orthogonal if their tangent lines are perpendicular at each point of
intersection of the curves.Show that the curves of the given equations are orthogonal.

Question 40

Question 41

Question 42

Question 43

Question 44

In an adiabatic process (one in which no heat transfer takes place), the pressure P and volume V of an ideal gas such as oxygen satisfy the equation

Question 45

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Question 48

.

Question 49

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Question 51

Question 52

Find the derivative of the function.

Question 53

The mass of the part of a metal rod that lies between its left end and a point x meters to the right is

Question 54

The cost (in dollars) of producing x units of a certain commodity is

Question 55

Question 56

Differentiate.

Question 57

Question 58

Question 59

Find the differential of the function at the indicated number.

Question 60

Question 61

Question 62

Question 63

Question 64

Find the derivative of the function.

Question 65

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Question 66

Find the derivative of the function.

Question 67

Question 68

Question 69

Question 70

Question 71

Question 72

Question 73

Find the derivative of the function.

Question 74

Question 75

Question 76