University Calculus: Early Transcendentals (4th Edition)
University Calculus: Early Transcendentals (4th Edition)
4th Edition
ISBN: 9780134995540
Author: Joel R. Hass, Christopher E. Heil, Przemyslaw Bogacki, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Concept explainers

Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the se…
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integratio…
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects th…
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
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Chapter 3.10, Problem 18E

(a)

To determine

Calculate the relationship between ds/dt to dx/dt,dy/dt and dz/dt.

(b)

To determine

Calculate the relationship between ds/dt to dy/dt and dz/dt if x is constant.

(c)

To determine

Calculate the relationship between dx/dt to dy/dt and dz/dt if s is constant.

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Chapter 3 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 3.1 - In Exercises 14, use the grid and a straight edge...Ch. 3.1 - In Exercises 1-4, use the grid and a straight edge...Ch. 3.1 - In Exercises 1−4, use the grid and a straight edge...Ch. 3.1 - In Exercises 1−4, use the grid and a straight edge...Ch. 3.1 - In Exercises510, find an equation for the tangent...Ch. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - In Exercises 5(10, find an equation for the...Ch. 3.1 - In Exercises 510, find an equation for the tangent...Ch. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - In Exercises 1118, find the slope of the...Ch. 3.1 - In Exercises 11–18, find the slope of the...Ch. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - In Exercises 11–18, find the slope of the...Ch. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - In Exercises 19–22, find the slope of the curve at...Ch. 3.1 - In Exercises 19–22, find the slope of the curve at...Ch. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Prob. 23ECh. 3.1 - Effectiveness of a drug On a scale from 0 to 1,...Ch. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Prob. 27ECh. 3.1 - Prob. 28ECh. 3.1 - Prob. 29ECh. 3.1 - Speed of a rocket At t sec after liftoff, the...Ch. 3.1 - Prob. 31ECh. 3.1 - Prob. 32ECh. 3.1 - Prob. 33ECh. 3.1 - Prob. 34ECh. 3.1 - Prob. 35ECh. 3.1 - Prob. 36ECh. 3.1 - We say that a continuous curve y = f(x) has a...Ch. 3.1 - Prob. 38ECh. 3.1 - Prob. 39ECh. 3.1 - Prob. 40ECh. 3.1 - Prob. 41ECh. 3.1 - Prob. 42ECh. 3.1 - Prob. 43ECh. 3.1 - Graph the curves in Exercises 39–48. Where do the...Ch. 3.1 - Prob. 45ECh. 3.1 - Prob. 46ECh. 3.1 - Prob. 47ECh. 3.1 - Prob. 48ECh. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Prob. 4ECh. 3.2 - Using the definition, calculate the derivatives of...Ch. 3.2 - Prob. 6ECh. 3.2 - In Exercises 712, find the indicated derivatives....Ch. 3.2 - In Exercises 7–12, find the indicated...Ch. 3.2 - Prob. 9ECh. 3.2 - Prob. 10ECh. 3.2 - Prob. 11ECh. 3.2 - In Exercises 7–12, find the indicated...Ch. 3.2 - Prob. 13ECh. 3.2 - Prob. 14ECh. 3.2 - Prob. 15ECh. 3.2 - In Exercises 13–16, differentiate the functions...Ch. 3.2 - In Exercises 17–18, differentiate the functions....Ch. 3.2 - Prob. 18ECh. 3.2 - In Exercises 19–22, find the values of the...Ch. 3.2 - Prob. 20ECh. 3.2 - In Exercises 19–22, find the values of the...Ch. 3.2 - Prob. 22ECh. 3.2 - Prob. 23ECh. 3.2 - Use the formula to find the derivative of the...Ch. 3.2 - Prob. 25ECh. 3.2 - Use the formula to find the derivative of the...Ch. 3.2 - Prob. 27ECh. 3.2 - Prob. 28ECh. 3.2 - Prob. 29ECh. 3.2 - Prob. 30ECh. 3.2 - Prob. 31ECh. 3.2 - Prob. 32ECh. 3.2 - Prob. 33ECh. 3.2 - Prob. 34ECh. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Compute the right-hand and left-hand derivatives...Ch. 3.2 - Prob. 38ECh. 3.2 - Prob. 39ECh. 3.2 - Prob. 40ECh. 3.2 - Prob. 41ECh. 3.2 - Prob. 42ECh. 3.2 - Prob. 43ECh. 3.2 - Prob. 44ECh. 3.2 - Each figure in Exercises 45-50 shows the graph of...Ch. 3.2 - Each figure in Exercises 45-50 shows the graph of...Ch. 3.2 - Each figure in Exercises 45-50 shows the graph of...Ch. 3.2 - Each figure in Exercises 45–50 shows the graph of...Ch. 3.2 - Prob. 49ECh. 3.2 - Prob. 50ECh. 3.2 - Prob. 51ECh. 3.2 - Prob. 52ECh. 3.2 - Prob. 53ECh. 3.2 - Prob. 54ECh. 3.2 - Prob. 55ECh. 3.2 - Prob. 56ECh. 3.2 - Prob. 57ECh. 3.2 - Prob. 58ECh. 3.2 - Prob. 59ECh. 3.2 - Prob. 60ECh. 3.2 - Prob. 61ECh. 3.2 - Prob. 62ECh. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Prob. 4ECh. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Prob. 8ECh. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Prob. 10ECh. 3.3 - Derivative Calculations In Exercises 112, find the...Ch. 3.3 - Prob. 12ECh. 3.3 - In Exercises 1316, find y'(a) by applying the...Ch. 3.3 - Prob. 14ECh. 3.3 - In Exercises 1316, find y' (a) by applying the...Ch. 3.3 - Prob. 16ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 18ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 24ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 26ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Prob. 32ECh. 3.3 - Prob. 33ECh. 3.3 - Prob. 34ECh. 3.3 - Prob. 35ECh. 3.3 - Prob. 36ECh. 3.3 - Prob. 37ECh. 3.3 - Prob. 38ECh. 3.3 - Prob. 39ECh. 3.3 - Find the derivatives of the functions in Exercises...Ch. 3.3 - Find the derivatives of all orders of the...Ch. 3.3 - Find the derivatives of all orders of the...Ch. 3.3 - Prob. 43ECh. 3.3 - Prob. 44ECh. 3.3 - Find the first and second derivatives of the...Ch. 3.3 - Prob. 46ECh. 3.3 - Prob. 47ECh. 3.3 - Prob. 48ECh. 3.3 - Prob. 49ECh. 3.3 - Prob. 50ECh. 3.3 - Prob. 51ECh. 3.3 - Prob. 52ECh. 3.3 - Prob. 53ECh. 3.3 - Prob. 54ECh. 3.3 - Prob. 55ECh. 3.3 - Prob. 56ECh. 3.3 - Prob. 57ECh. 3.3 - Prob. 58ECh. 3.3 - Prob. 59ECh. 3.3 - Prob. 60ECh. 3.3 - Prob. 61ECh. 3.3 - Prob. 62ECh. 3.3 - Prob. 63ECh. 3.3 - Prob. 64ECh. 3.3 - Prob. 65ECh. 3.3 - Prob. 66ECh. 3.3 - Prob. 67ECh. 3.3 - Prob. 68ECh. 3.3 - Prob. 69ECh. 3.3 - Prob. 70ECh. 3.3 - Prob. 71ECh. 3.3 - Prob. 72ECh. 3.3 - Prob. 73ECh. 3.3 - Prob. 74ECh. 3.3 - Prob. 75ECh. 3.3 - The Reciprocal Rule The Reciprocal Rule says that...Ch. 3.3 - Prob. 77ECh. 3.3 - Prob. 78ECh. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.4 - Exercises 16 give the positions s = f(t) of a body...Ch. 3.4 - Exercises 1–6 give the positions s = f(t) of a...Ch. 3.4 - Prob. 3ECh. 3.4 - Exercises 1–6 give the positions s = f(t) of a...Ch. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Particle motion At time t, the position of a body...Ch. 3.4 - Particle motion At time t ≥ 0, the velocity of a...Ch. 3.4 - Free fall on Mars and Jupiter The equations for...Ch. 3.4 - Prob. 10ECh. 3.4 - Prob. 11ECh. 3.4 - Speeding bullet A 45-caliber bullet shot straight...Ch. 3.4 - Free fall from the Tower of Pisa Had Galileo...Ch. 3.4 - Prob. 14ECh. 3.4 - Prob. 15ECh. 3.4 - A particle P moves on the number line shown in...Ch. 3.4 - Prob. 17ECh. 3.4 - Prob. 18ECh. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Body surface area A typical male’s body surface...Ch. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 3.4 - Prob. 27ECh. 3.4 - Inflating a balloon The volume V = (4/3)πr3 of a...Ch. 3.4 - Prob. 29ECh. 3.4 - Volcanic lava fountains Although the November 1959...Ch. 3.4 - Prob. 31ECh. 3.4 - Prob. 32ECh. 3.4 - Exercises 31–34 give the position function s =...Ch. 3.4 - Prob. 34ECh. 3.5 - In Exercises 1–18, find dy/dx. 1. y = −10x + 3 cos...Ch. 3.5 - In Exercises 1–18, find dy/dx. 2. Ch. 3.5 - In Exercises 118, find dy/dx. 3. y = x2cos xCh. 3.5 - Prob. 4ECh. 3.5 - In Exercises 118, find dy/dx. 5. y=cscx4x+7exCh. 3.5 - Prob. 6ECh. 3.5 - In Exercises 118, find dy/dx. 7. f(x) = sin x tan...Ch. 3.5 - Prob. 8ECh. 3.5 - In Exercises 1–18, find dy/dx. 9. Ch. 3.5 - Prob. 10ECh. 3.5 - Prob. 11ECh. 3.5 - Prob. 12ECh. 3.5 - Prob. 13ECh. 3.5 - Prob. 14ECh. 3.5 - Prob. 15ECh. 3.5 - Prob. 16ECh. 3.5 - Prob. 17ECh. 3.5 - Prob. 18ECh. 3.5 - Prob. 19ECh. 3.5 - Prob. 20ECh. 3.5 - Prob. 21ECh. 3.5 - Prob. 22ECh. 3.5 - Prob. 23ECh. 3.5 - Prob. 24ECh. 3.5 - Prob. 25ECh. 3.5 - Prob. 26ECh. 3.5 - Prob. 27ECh. 3.5 - Prob. 28ECh. 3.5 - Prob. 29ECh. 3.5 - Prob. 30ECh. 3.5 - Prob. 31ECh. 3.5 - Prob. 32ECh. 3.5 - Prob. 33ECh. 3.5 - Prob. 34ECh. 3.5 - Prob. 35ECh. 3.5 - Prob. 36ECh. 3.5 - Prob. 37ECh. 3.5 - Prob. 38ECh. 3.5 - Do the graphs of the functions in Exercises 39–44...Ch. 3.5 - Do the graphs of the functions in Exercises 39–44...Ch. 3.5 - Do the graphs of the functions in Exercises 39–44...Ch. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - The equations in Exercises 57 and 58 give the...Ch. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Prob. 60ECh. 3.5 - Prob. 61ECh. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - Prob. 69ECh. 3.5 - Prob. 70ECh. 3.6 - Derivative Calculations In Exercises 18, given y =...Ch. 3.6 - Derivative Calculations In Exercises 1–8, given y...Ch. 3.6 - Derivative Calculation In Exercises 1–8, given y =...Ch. 3.6 - Derivative Calculations In Exercises 1–8, given y...Ch. 3.6 - Derivation Calculations In Exercises 1–8, given y...Ch. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Derivative Calculations In Exercises 1–8, given y...Ch. 3.6 - In Exercises 922, write the function in the form y...Ch. 3.6 - Prob. 10ECh. 3.6 - In Exercises 922, write the function in the form y...Ch. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - In Exercises 922, write the function in the form y...Ch. 3.6 - Prob. 14ECh. 3.6 - In Exercises 922, write the function in the form y...Ch. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - In Exercises 9–22, write the function in the form...Ch. 3.6 - In Exercises 922, write the function in the form y...Ch. 3.6 - Prob. 22ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 34ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 38ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Find the derivatives of the functions in Exercises...Ch. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - In Exercises 51–70, find dy/dt. 52. y = sec2 πt Ch. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - In Exercises 51–70, find dy/dt. 56. y = (t−3/4 sin...Ch. 3.6 - Prob. 57ECh. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - In Exercises 51–70, find dy/dt. 60. Ch. 3.6 - Prob. 61ECh. 3.6 - Prob. 62ECh. 3.6 - Prob. 63ECh. 3.6 - In Exercises 51–70, find dy/dt. 64. Ch. 3.6 - Prob. 65ECh. 3.6 - Prob. 66ECh. 3.6 - Prob. 67ECh. 3.6 - In Exercises 51–70, find dy/dt. 68. y = cos4(sec2...Ch. 3.6 - Prob. 69ECh. 3.6 - Prob. 70ECh. 3.6 - Prob. 71ECh. 3.6 - Second Derivatives Find y″ in Exercises 71–78. 72....Ch. 3.6 - Prob. 73ECh. 3.6 - Prob. 74ECh. 3.6 - Prob. 75ECh. 3.6 - Second Derivatives Find y″ in Exercises 71–78. 76....Ch. 3.6 - Prob. 77ECh. 3.6 - Prob. 78ECh. 3.6 - Prob. 79ECh. 3.6 - For each of the following functions, solve both...Ch. 3.6 - Finding Derivative values In Exercises 81–86, find...Ch. 3.6 - Prob. 82ECh. 3.6 - Prob. 83ECh. 3.6 - Finding Derivative values In Exercises 81–86, find...Ch. 3.6 - Prob. 85ECh. 3.6 - Prob. 86ECh. 3.6 - Prob. 87ECh. 3.6 - If r = sin(f(t)), f(0) = π/3, and f′(0) = 4, then...Ch. 3.6 - Prob. 89ECh. 3.6 - Prob. 90ECh. 3.6 - Prob. 91ECh. 3.6 - Prob. 92ECh. 3.6 - Prob. 93ECh. 3.6 - Prob. 94ECh. 3.6 - Prob. 95ECh. 3.6 - Find the tangent line to at x = 2. Ch. 3.6 - Find the tangent line to the curve at x =...Ch. 3.6 - Prob. 98ECh. 3.6 - Prob. 99ECh. 3.6 - The graph in the accompanying figure shows the...Ch. 3.6 - Prob. 101ECh. 3.6 - Prob. 102ECh. 3.6 - Prob. 103ECh. 3.6 - Prob. 104ECh. 3.6 - Prob. 105ECh. 3.6 - Prob. 106ECh. 3.6 - Prob. 107ECh. 3.6 - Prob. 108ECh. 3.6 - Using the Chain Rule, show that the Power Rule...Ch. 3.6 - Prob. 110ECh. 3.6 - Prob. 111ECh. 3.6 - Prob. 112ECh. 3.6 - Verify each of the following statements. If f is...Ch. 3.6 - Prob. 114ECh. 3.6 - Prob. 115ECh. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Prob. 5ECh. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Differentiating implicitly Use implicit...Ch. 3.7 - Prob. 10ECh. 3.7 - Prob. 11ECh. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Prob. 13ECh. 3.7 - Prob. 14ECh. 3.7 - Prob. 15ECh. 3.7 - Differentiating Implicitly Use implicit...Ch. 3.7 - Find dr/dθ in Exercises 17-20. Ch. 3.7 - Prob. 18ECh. 3.7 - Find dr / d in Exercises 17–20. Ch. 3.7 - Find dr / d in Exercises 17–20. cos r + cot =...Ch. 3.7 - In Exercises 21−28, use implicit differentiation...Ch. 3.7 - Prob. 22ECh. 3.7 - In Exercises 21–28, use implicit differentiation...Ch. 3.7 - In Exercises 21–28, use implicit differentiation...Ch. 3.7 - Prob. 25ECh. 3.7 - Prob. 26ECh. 3.7 - Prob. 27ECh. 3.7 - In Exercises 21–28, use implicit differentiation...Ch. 3.7 - Prob. 29ECh. 3.7 - If , find the value of at the point (0, –1). Ch. 3.7 - Prob. 31ECh. 3.7 - In Exercises 31 and 32, find the slope of the...Ch. 3.7 - Prob. 33ECh. 3.7 - Prob. 34ECh. 3.7 - Prob. 35ECh. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Prob. 37ECh. 3.7 - Prob. 38ECh. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Exercises 33–42, verify that the given point is on...Ch. 3.7 - Prob. 41ECh. 3.7 - In Exercises 33−42, verify that the given point is...Ch. 3.7 - Prob. 43ECh. 3.7 - Normal lines parallel to a line Find the normal...Ch. 3.7 - Prob. 45ECh. 3.7 - Prob. 46ECh. 3.7 - Prob. 47ECh. 3.7 - Prob. 48ECh. 3.7 - Prob. 49ECh. 3.7 - Prob. 50ECh. 3.7 - Prob. 51ECh. 3.7 - Prob. 52ECh. 3.7 - Prob. 53ECh. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.7 - Prob. 57ECh. 3.7 - Prob. 58ECh. 3.8 - In Exercises 1–4: Find f–1(x). Graph f and f–1...Ch. 3.8 - Prob. 2ECh. 3.8 - Prob. 3ECh. 3.8 - Prob. 4ECh. 3.8 - Prob. 5ECh. 3.8 - Prob. 6ECh. 3.8 - Prob. 7ECh. 3.8 - Prob. 8ECh. 3.8 - Prob. 9ECh. 3.8 - Prob. 10ECh. 3.8 - Derivatives of Logarithms In Exercises 1140, find...Ch. 3.8 - Prob. 12ECh. 3.8 - Derivatives of Logarithms In Exercises 1140, find...Ch. 3.8 - Derivatives of Logarithms In Exercises 11–40, find...Ch. 3.8 - Derivatives of Logarithms In Exercises 1140, find...Ch. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Prob. 18ECh. 3.8 - Derivatives of Logarithms In Exercises 11-40, find...Ch. 3.8 - Prob. 20ECh. 3.8 - Derivatives of Logarithms In Exercises 11-40, find...Ch. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Prob. 29ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - In Exercises 11-40, find the derivative of y with...Ch. 3.8 - Prob. 39ECh. 3.8 - Prob. 40ECh. 3.8 - Prob. 41ECh. 3.8 - Prob. 42ECh. 3.8 - Prob. 43ECh. 3.8 - Prob. 44ECh. 3.8 - Prob. 45ECh. 3.8 - Prob. 46ECh. 3.8 - Prob. 47ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - Prob. 49ECh. 3.8 - Prob. 50ECh. 3.8 - Prob. 51ECh. 3.8 - Prob. 52ECh. 3.8 - Prob. 53ECh. 3.8 - In Exercises 41-54, use logarithmic...Ch. 3.8 - In Exercises 55-62, find the derivative of y with...Ch. 3.8 - In Exercises 55-62, find the derivative of y with...Ch. 3.8 - In Exercises 55-62, find the derivative of y with...Ch. 3.8 - Prob. 58ECh. 3.8 - Prob. 59ECh. 3.8 - Prob. 60ECh. 3.8 - Prob. 61ECh. 3.8 - Prob. 62ECh. 3.8 - Prob. 63ECh. 3.8 - Prob. 64ECh. 3.8 - Prob. 65ECh. 3.8 - Prob. 66ECh. 3.8 - Prob. 67ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 70ECh. 3.8 - Prob. 71ECh. 3.8 - Prob. 72ECh. 3.8 - Prob. 73ECh. 3.8 - Prob. 74ECh. 3.8 - Prob. 75ECh. 3.8 - Prob. 76ECh. 3.8 - Prob. 77ECh. 3.8 - Prob. 78ECh. 3.8 - Prob. 79ECh. 3.8 - Prob. 80ECh. 3.8 - Prob. 81ECh. 3.8 - In Exercises 67-88, find the derivative of y with...Ch. 3.8 - Prob. 83ECh. 3.8 - Prob. 84ECh. 3.8 - Prob. 85ECh. 3.8 - Prob. 86ECh. 3.8 - Prob. 87ECh. 3.8 - Prob. 88ECh. 3.8 - Prob. 89ECh. 3.8 - Prob. 90ECh. 3.8 - Prob. 91ECh. 3.8 - Prob. 92ECh. 3.8 - Prob. 93ECh. 3.8 - Prob. 94ECh. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - Prob. 96ECh. 3.8 - In Exercises 89−100, use logarithmic...Ch. 3.8 - Prob. 98ECh. 3.8 - Prob. 99ECh. 3.8 - Prob. 100ECh. 3.8 - Prob. 101ECh. 3.8 - Prob. 102ECh. 3.8 - Prob. 103ECh. 3.8 - Prob. 104ECh. 3.9 - Use reference triangles in an appropriate...Ch. 3.9 - Prob. 2ECh. 3.9 - Prob. 3ECh. 3.9 - Prob. 4ECh. 3.9 - Prob. 5ECh. 3.9 - Prob. 6ECh. 3.9 - Prob. 7ECh. 3.9 - Prob. 8ECh. 3.9 - Prob. 9ECh. 3.9 - Prob. 10ECh. 3.9 - Prob. 11ECh. 3.9 - Prob. 12ECh. 3.9 - Prob. 13ECh. 3.9 - Prob. 14ECh. 3.9 - Prob. 15ECh. 3.9 - Prob. 16ECh. 3.9 - Prob. 17ECh. 3.9 - Prob. 18ECh. 3.9 - Prob. 19ECh. 3.9 - Prob. 20ECh. 3.9 - In Exercises 2142, find the derivative of y with...Ch. 3.9 - Prob. 22ECh. 3.9 - Prob. 23ECh. 3.9 - Prob. 24ECh. 3.9 - Prob. 25ECh. 3.9 - Prob. 26ECh. 3.9 - Prob. 27ECh. 3.9 - Prob. 28ECh. 3.9 - Prob. 29ECh. 3.9 - Prob. 30ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - Prob. 33ECh. 3.9 - Prob. 34ECh. 3.9 - Prob. 35ECh. 3.9 - Prob. 36ECh. 3.9 - Prob. 37ECh. 3.9 - Prob. 38ECh. 3.9 - Prob. 39ECh. 3.9 - Prob. 40ECh. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - In Exercises 21–42, find the derivative of y with...Ch. 3.9 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - Prob. 46ECh. 3.9 - Prob. 47ECh. 3.9 - Prob. 48ECh. 3.9 - Prob. 49ECh. 3.9 - Prob. 50ECh. 3.9 - Prob. 51ECh. 3.9 - Prob. 52ECh. 3.9 - Prob. 53ECh. 3.9 - Prob. 54ECh. 3.9 - Prob. 55ECh. 3.9 - Prob. 56ECh. 3.9 - Prob. 57ECh. 3.9 - Prob. 58ECh. 3.9 - Prob. 59ECh. 3.9 - Prob. 60ECh. 3.9 - Prob. 61ECh. 3.9 - Prob. 62ECh. 3.9 - Prob. 63ECh. 3.9 - Prob. 64ECh. 3.9 - Prob. 65ECh. 3.9 - Prob. 66ECh. 3.9 - Prob. 67ECh. 3.9 - Prob. 68ECh. 3.9 - Prob. 69ECh. 3.9 - Prob. 70ECh. 3.10 - Area Suppose that the radius r and area A = pr2of...Ch. 3.10 - Surface area Suppose that the radius r and surface...Ch. 3.10 - Prob. 3ECh. 3.10 - Prob. 4ECh. 3.10 - Prob. 5ECh. 3.10 - Prob. 6ECh. 3.10 - Prob. 7ECh. 3.10 - Prob. 8ECh. 3.10 - Prob. 9ECh. 3.10 - If r + s2 + v3 = 12, dr/dt = 4, and ds/dt = −3,...Ch. 3.10 - Prob. 11ECh. 3.10 - Prob. 12ECh. 3.10 - Prob. 13ECh. 3.10 - Prob. 14ECh. 3.10 - Prob. 15ECh. 3.10 - Prob. 16ECh. 3.10 - Distance Let x and y be functions of t, and let ...Ch. 3.10 - Diagonals If x, y, and z are lengths of the edges...Ch. 3.10 - Area The area A of a triangle with sides of...Ch. 3.10 - Prob. 20ECh. 3.10 - Changing dimensions in a rectangle The length l of...Ch. 3.10 - Prob. 22ECh. 3.10 - Prob. 23ECh. 3.10 - Prob. 24ECh. 3.10 - Prob. 25ECh. 3.10 - Prob. 26ECh. 3.10 - Prob. 27ECh. 3.10 - A draining conical reservoir Water is flowing at...Ch. 3.10 - Prob. 29ECh. 3.10 - Prob. 30ECh. 3.10 - Prob. 31ECh. 3.10 - Prob. 32ECh. 3.10 - A balloon and a bicycle A balloon is rising...Ch. 3.10 - Prob. 34ECh. 3.10 - Prob. 35ECh. 3.10 - Prob. 36ECh. 3.10 - Prob. 37ECh. 3.10 - Videotaping a moving car You are videotaping a...Ch. 3.10 - Prob. 39ECh. 3.10 - Prob. 40ECh. 3.10 - Prob. 41ECh. 3.10 - Prob. 42ECh. 3.10 - Baseball players A baseball diamond is a square 90...Ch. 3.10 - Prob. 44ECh. 3.10 - Prob. 45ECh. 3.10 - Prob. 46ECh. 3.10 - Prob. 47ECh. 3.11 - Prob. 1ECh. 3.11 - Prob. 2ECh. 3.11 - Prob. 3ECh. 3.11 - Prob. 4ECh. 3.11 - Prob. 5ECh. 3.11 - Prob. 6ECh. 3.11 - Prob. 7ECh. 3.11 - Prob. 8ECh. 3.11 - Prob. 9ECh. 3.11 - Prob. 10ECh. 3.11 - Prob. 11ECh. 3.11 - Prob. 12ECh. 3.11 - Prob. 13ECh. 3.11 - Prob. 14ECh. 3.11 - Prob. 15ECh. 3.11 - Prob. 16ECh. 3.11 - Prob. 17ECh. 3.11 - Prob. 18ECh. 3.11 - Prob. 19ECh. 3.11 - Prob. 20ECh. 3.11 - Prob. 21ECh. 3.11 - Prob. 22ECh. 3.11 - Prob. 23ECh. 3.11 - Prob. 24ECh. 3.11 - Prob. 25ECh. 3.11 - Prob. 26ECh. 3.11 - Prob. 27ECh. 3.11 - Prob. 28ECh. 3.11 - Prob. 29ECh. 3.11 - Prob. 30ECh. 3.11 - Prob. 31ECh. 3.11 - Prob. 32ECh. 3.11 - Prob. 33ECh. 3.11 - Prob. 34ECh. 3.11 - Prob. 35ECh. 3.11 - Prob. 36ECh. 3.11 - Prob. 37ECh. 3.11 - Prob. 38ECh. 3.11 - Prob. 39ECh. 3.11 - Prob. 40ECh. 3.11 - Prob. 41ECh. 3.11 - Prob. 42ECh. 3.11 - Prob. 43ECh. 3.11 - Prob. 44ECh. 3.11 - Prob. 45ECh. 3.11 - Prob. 46ECh. 3.11 - Prob. 47ECh. 3.11 - Prob. 48ECh. 3.11 - Prob. 49ECh. 3.11 - Prob. 50ECh. 3.11 - Prob. 51ECh. 3.11 - Prob. 52ECh. 3.11 - Prob. 53ECh. 3.11 - Prob. 54ECh. 3.11 - Prob. 55ECh. 3.11 - Prob. 56ECh. 3.11 - Prob. 57ECh. 3.11 - Prob. 58ECh. 3.11 - Prob. 59ECh. 3.11 - Prob. 60ECh. 3.11 - Prob. 61ECh. 3.11 - Prob. 62ECh. 3.11 - Prob. 63ECh. 3.11 - Prob. 64ECh. 3.11 - Prob. 65ECh. 3.11 - Prob. 66ECh. 3.11 - Prob. 67ECh. 3.11 - Prob. 68ECh. 3 - Prob. 1GYRCh. 3 - What role does the derivative play in defining...Ch. 3 - Prob. 3GYRCh. 3 - Prob. 4GYRCh. 3 - Prob. 5GYRCh. 3 - Prob. 6GYRCh. 3 - Prob. 7GYRCh. 3 - Prob. 8GYRCh. 3 - Prob. 9GYRCh. 3 - Prob. 10GYRCh. 3 - Prob. 11GYRCh. 3 - Prob. 12GYRCh. 3 - Prob. 13GYRCh. 3 - Prob. 14GYRCh. 3 - Prob. 15GYRCh. 3 - Prob. 16GYRCh. 3 - Prob. 17GYRCh. 3 - Prob. 18GYRCh. 3 - Prob. 19GYRCh. 3 - Prob. 20GYRCh. 3 - Prob. 21GYRCh. 3 - Prob. 22GYRCh. 3 - What is the derivative of the natural logarithm...Ch. 3 - Prob. 24GYRCh. 3 - Prob. 25GYRCh. 3 - Prob. 26GYRCh. 3 - Prob. 27GYRCh. 3 - Prob. 28GYRCh. 3 - Prob. 29GYRCh. 3 - Prob. 30GYRCh. 3 - Outline a strategy for solving related rates...Ch. 3 - Prob. 32GYRCh. 3 - Prob. 33GYRCh. 3 - Prob. 1PECh. 3 - Prob. 2PECh. 3 - Prob. 3PECh. 3 - Prob. 4PECh. 3 - Prob. 5PECh. 3 - Prob. 6PECh. 3 - Prob. 7PECh. 3 - Prob. 8PECh. 3 - Prob. 9PECh. 3 - Prob. 10PECh. 3 - Prob. 11PECh. 3 - Prob. 12PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 14PECh. 3 - Prob. 15PECh. 3 - Prob. 16PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 18PECh. 3 - Prob. 19PECh. 3 - Prob. 20PECh. 3 - Prob. 21PECh. 3 - Prob. 22PECh. 3 - Prob. 23PECh. 3 - Prob. 24PECh. 3 - Prob. 25PECh. 3 - Prob. 26PECh. 3 - Prob. 27PECh. 3 - Prob. 28PECh. 3 - Prob. 29PECh. 3 - Prob. 30PECh. 3 - Prob. 31PECh. 3 - Prob. 32PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 34PECh. 3 - Prob. 35PECh. 3 - Prob. 36PECh. 3 - Prob. 37PECh. 3 - Prob. 38PECh. 3 - Prob. 39PECh. 3 - Prob. 40PECh. 3 - Prob. 41PECh. 3 - Prob. 42PECh. 3 - Prob. 43PECh. 3 - Prob. 44PECh. 3 - Prob. 45PECh. 3 - Prob. 46PECh. 3 - Prob. 47PECh. 3 - Prob. 48PECh. 3 - Prob. 49PECh. 3 - Prob. 50PECh. 3 - Prob. 51PECh. 3 - Prob. 52PECh. 3 - Prob. 53PECh. 3 - Find the derivatives of the functions in Exercises...Ch. 3 - Prob. 55PECh. 3 - Prob. 56PECh. 3 - Prob. 57PECh. 3 - Prob. 58PECh. 3 - Prob. 59PECh. 3 - Prob. 60PECh. 3 - Prob. 61PECh. 3 - Prob. 62PECh. 3 - Prob. 63PECh. 3 - Prob. 64PECh. 3 - Prob. 65PECh. 3 - Prob. 66PECh. 3 - Prob. 67PECh. 3 - Prob. 68PECh. 3 - Prob. 69PECh. 3 - Prob. 70PECh. 3 - Prob. 71PECh. 3 - Prob. 72PECh. 3 - Prob. 73PECh. 3 - Prob. 74PECh. 3 - Prob. 75PECh. 3 - Prob. 76PECh. 3 - Prob. 77PECh. 3 - Prob. 78PECh. 3 - Prob. 79PECh. 3 - Prob. 80PECh. 3 - In Exercises 81 and 82, find dr / ds. 81. r cos 2s...Ch. 3 - Prob. 82PECh. 3 - Prob. 83PECh. 3 - Prob. 84PECh. 3 - Prob. 85PECh. 3 - Prob. 86PECh. 3 - Prob. 87PECh. 3 - Prob. 88PECh. 3 - Prob. 89PECh. 3 - Prob. 90PECh. 3 - Prob. 91PECh. 3 - Prob. 92PECh. 3 - Prob. 93PECh. 3 - Prob. 94PECh. 3 - Prob. 95PECh. 3 - Prob. 96PECh. 3 - Prob. 97PECh. 3 - Prob. 98PECh. 3 - Prob. 99PECh. 3 - Prob. 100PECh. 3 - Prob. 101PECh. 3 - Prob. 102PECh. 3 - Prob. 103PECh. 3 - Prob. 104PECh. 3 - Prob. 105PECh. 3 - Prob. 106PECh. 3 - Prob. 107PECh. 3 - Prob. 108PECh. 3 - Prob. 109PECh. 3 - Prob. 110PECh. 3 - Prob. 111PECh. 3 - Prob. 112PECh. 3 - Prob. 113PECh. 3 - Prob. 114PECh. 3 - Prob. 115PECh. 3 - Prob. 116PECh. 3 - Prob. 117PECh. 3 - Prob. 118PECh. 3 - Prob. 119PECh. 3 - Prob. 120PECh. 3 - Prob. 121PECh. 3 - Prob. 122PECh. 3 - Prob. 123PECh. 3 - Prob. 124PECh. 3 - Prob. 125PECh. 3 - Prob. 126PECh. 3 - Prob. 127PECh. 3 - Prob. 128PECh. 3 - Prob. 129PECh. 3 - Prob. 130PECh. 3 - Prob. 131PECh. 3 - Prob. 132PECh. 3 - Prob. 133PECh. 3 - Prob. 134PECh. 3 - Prob. 135PECh. 3 - Prob. 136PECh. 3 - Prob. 137PECh. 3 - Prob. 138PECh. 3 - Prob. 139PECh. 3 - Prob. 140PECh. 3 - Prob. 141PECh. 3 - Prob. 142PECh. 3 - Prob. 143PECh. 3 - Prob. 144PECh. 3 - Prob. 145PECh. 3 - Prob. 146PECh. 3 - Draining a tank Water drains from the conical tank...Ch. 3 - Prob. 148PECh. 3 - Prob. 149PECh. 3 - Prob. 150PECh. 3 - Prob. 151PECh. 3 - Prob. 152PECh. 3 - Prob. 153PECh. 3 - Prob. 154PECh. 3 - Prob. 155PECh. 3 - Prob. 156PECh. 3 - Prob. 157PECh. 3 - Prob. 158PECh. 3 - Prob. 1AAECh. 3 - Prob. 2AAECh. 3 - Prob. 3AAECh. 3 - Prob. 4AAECh. 3 - Prob. 5AAECh. 3 - Prob. 6AAECh. 3 - Prob. 7AAECh. 3 - Prob. 8AAECh. 3 - Prob. 9AAECh. 3 - Prob. 10AAECh. 3 - Prob. 11AAECh. 3 - Prob. 12AAECh. 3 - Prob. 13AAECh. 3 - Prob. 14AAECh. 3 - Prob. 15AAECh. 3 - Prob. 16AAECh. 3 - Prob. 17AAECh. 3 - Prob. 18AAECh. 3 - Prob. 19AAECh. 3 - Prob. 20AAECh. 3 - Prob. 21AAECh. 3 - Prob. 22AAECh. 3 - Suppose that the functions f and g are defined...Ch. 3 - (Continuation of Exercise 23.) Use the result of...Ch. 3 - Prob. 25AAECh. 3 - Prob. 26AAECh. 3 - Prob. 27AAECh. 3 - Prob. 28AAECh. 3 - Prob. 29AAECh. 3 - Prob. 30AAECh. 3 - Prob. 31AAECh. 3 - Prob. 32AAE
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Area Between The Curve Problem No 1 - Applications Of Definite Integration - Diploma Maths II; Author: Ekeeda;https://www.youtube.com/watch?v=q3ZU0GnGaxA;License: Standard YouTube License, CC-BY