Deck 6: Applications of Integration

Question 1

Use the graph of y = ln x as an aid to sketch the graph of the function.

Answer 1

Question 2

Find the absolute extrema of the function on the indicated interval.

Answer 2

Question 3

Find the integral.

Answer 3

Question 4

Find the inverse function.

Question 5

Use logarithmic differentiation to find the derivative of the function.

Question 6

Use the properties of logarithms to expand the quantity.

Question 7

Find the given integral.

Question 8

Find the points of intersection of the graphs of the functions.Express your answers accurate to five
decimal places.

Question 9

Solve each equation for x.

Question 10

Question 11

Use logarithmic differentiation to find the derivative of the function.

Question 12

Question 13

Question 14

Question 15

Question 16

Find the solution of the equation correct to four decimal places.

Question 17

Differentiate the function.

Question 18

Question 19

Write the expression in algebraic form.

Question 20

Find the integral.

Question 21

Find the absolute minimum value of the function.

Question 22

Question 23

Question 24

Find the solution of the equation correct to four decimal places.

Question 25

Solve each equation for x.

Question 26

Use transformations to sketch the graph of the function.

Question 27

Question 28

Question 29

Solve the equation for x.

Question 30

Use the properties of logarithms to expand the quantity.

Question 31

Question 32

Evaluate the integral.

Question 33

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

Question 34

Use logarithmic differentiation to find the derivative of the function.

Question 35

Evaluate the integral.

Question 36

Differentiate the function.

Question 37

Find the solution of the equation correct to four decimal places.

Question 38

Differentiate the function.

Question 39

Question 40

Find the limit.

Question 41

Find the derivative of the function.

Question 42

Question 43

Question 44

Use the laws of logarithms to write the expression as the logarithm of a single quantity.

Question 45

Question 46

Question 47

Find the volume of the solid obtained by rotating about the y axis the region bounded by the curves.

Question 48

Question 49

Evaluate the integral to three decimal places.

Question 50

Question 51

Question 52

Question 53

Evaluate the given integral.

Question 54

Differentiate the function.

Question 55

Question 56

Question 57

Question 58

Find the limit.

Question 59

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question 60

Question 61

Simplify the expression.

Question 62

Evaluate the integral to three decimal places.

Question 63

Question 64

Find the limit.

Question 65

Use the laws of logarithms to write the expression as the logarithm of a single quantity.

Question 66

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.

Question 67

Evaluate the expression.

Question 68

Differentiate the function.

Question 69

Question 70

Question 71

Use the laws of logarithms to expand the expression.

Question 72

Question 73

Question 74

Question 75

Use the properties of logarithms to expand the quantity.

Question 76

Question 77

Differentiate the function.

Question 78