University Calculus
4th Edition
ISBN: 9780135164846
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas, Jr., Przemyslaw Bogacki
Publisher: PEARSON
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Chapter 3, Problem 23GYR
To determine
To explain the derivative of a natural logarithm function
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Chapter 3 Solutions
University Calculus
Ch. 3.1 - Slopes and Tangent Lines In exercises 1-4, use the...Ch. 3.1 - Prob. 2ECh. 3.1 - Prob. 3ECh. 3.1 - Prob. 4ECh. 3.1 - Prob. 5ECh. 3.1 - Prob. 6ECh. 3.1 - Prob. 7ECh. 3.1 - Prob. 8ECh. 3.1 - Prob. 9ECh. 3.1 - Prob. 10E
Ch. 3.1 - Prob. 11ECh. 3.1 - Prob. 12ECh. 3.1 - Prob. 13ECh. 3.1 - Prob. 14ECh. 3.1 - Prob. 15ECh. 3.1 - Prob. 16ECh. 3.1 - Prob. 17ECh. 3.1 - Prob. 18ECh. 3.1 - Prob. 19ECh. 3.1 - Prob. 20ECh. 3.1 - Prob. 21ECh. 3.1 - Prob. 22ECh. 3.1 - Interpreting Derivative Values
23. Growth Of The...Ch. 3.1 - Effectiveness of a drug On a scale 0 to 1, the...Ch. 3.1 - Prob. 25ECh. 3.1 - Prob. 26ECh. 3.1 - Find equations of all lines having slope -1 that...Ch. 3.1 - Find an equation of the straight line having slope...Ch. 3.1 - Rates of change Object dropped from the tower An...Ch. 3.1 - Speed of a rocket At t sec after liftoff, the...Ch. 3.1 - 31. Circle’s changing area
What is the rate of...Ch. 3.1 - Rates of changes Balls changing volume What is the...Ch. 3.1 - Rates of changes Show that the line y=mx+b Is its...Ch. 3.1 - Rates of change
34. Find the slope of the tangent...Ch. 3.1 - Testing for tangent lines
35. Does the graph of...Ch. 3.1 - Testing for Tangent Lines
36. Does the graph...Ch. 3.1 - Does the graph of f(x)={1,x00,x=01,x0 Have a...Ch. 3.1 - Does the graph of U(x)={0,x01,x0 Have a vertical...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - T Graph the curve in Exercises 39-48. Where do the...Ch. 3.1 - T Graph the curve in Exercises 39-48. Where do the...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - T Graph the curve in Exercises 39-48. Where do the...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - T Graph the curve in Exercises 39-48. Where do the...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - T
Graph the curve in Exercises 39-48.
Where do...Ch. 3.1 - COMPUTER EXPLORATIONS Use a CAS to perform the...Ch. 3.1 - COMPUTER EXPLORATIONS Use a CAS to perform the...Ch. 3.1 - COMPUTER EXPLORATIONS
Use a CAS to perform the...Ch. 3.1 - COMPUTER EXPLORATIONS Use a CAS to perform the...Ch. 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 - 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 - In Exercises 7-12, find the indicated derivatives....Ch. 3.2 - In Exercises 7-12, find the indicated...Ch. 3.2 - In Exercises 7-12, find the indicated derivatives....Ch. 3.2 - In Exercises 7-12, find the indicated...Ch. 3.2 - In Exercises 7-12, find the indicated...Ch. 3.2 - In Exercises 7-12, find the indicated...Ch. 3.2 - In Exercises 13-16, differentiate the functions...Ch. 3.2 - In Exercises 13-16, differentiate the functions...Ch. 3.2 - In Exercises 13-16, differentiate the functions...Ch. 3.2 - In Exercises 13-16, differentiate the functions...Ch. 3.2 - In Exercises 17-18, differentiate the functions....Ch. 3.2 - In Exercises 17-18, differentiate the functions....Ch. 3.2 - In Exercises 19-22, find the values of the...Ch. 3.2 - In Exercises 19-22, find the values of the...Ch. 3.2 - In Exercises 19-22, find the values of the...Ch. 3.2 - In Exercises 19-22, find the values of the...Ch. 3.2 - Prob. 23ECh. 3.2 - Prob. 24ECh. 3.2 - Prob. 25ECh. 3.2 - Prob. 26ECh. 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 - 33. Growth in the economy The graph in the...Ch. 3.2 - Fruit flies (Continuation of Example 4, Section...Ch. 3.2 - Prob. 35ECh. 3.2 - Prob. 36ECh. 3.2 - Prob. 37ECh. 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 - Prob. 45ECh. 3.2 - Prob. 46ECh. 3.2 - Prob. 47ECh. 3.2 - Prob. 48ECh. 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 - 57. Derivative of Does knowing that function is...Ch. 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 - 64. Weierstrass’s nowhere differentiable...Ch. 3.2 - Prob. 65ECh. 3.2 - Prob. 66ECh. 3.2 - Prob. 69ECh. 3.2 - COMPUTER EXPLORATIONS
Use a CAS to perform the...Ch. 3.3 - Prob. 1ECh. 3.3 - Prob. 2ECh. 3.3 - Prob. 3ECh. 3.3 - Prob. 4ECh. 3.3 - Prob. 5ECh. 3.3 - Prob. 6ECh. 3.3 - Prob. 7ECh. 3.3 - Prob. 8ECh. 3.3 - Prob. 9ECh. 3.3 - Prob. 10ECh. 3.3 - Prob. 11ECh. 3.3 - Prob. 12ECh. 3.3 - Prob. 13ECh. 3.3 - Prob. 14ECh. 3.3 - Prob. 15ECh. 3.3 - Prob. 16ECh. 3.3 - Prob. 17ECh. 3.3 - Prob. 18ECh. 3.3 - Prob. 19ECh. 3.3 - Prob. 20ECh. 3.3 - Prob. 21ECh. 3.3 - Prob. 22ECh. 3.3 - Prob. 23ECh. 3.3 - Prob. 24ECh. 3.3 - Prob. 25ECh. 3.3 - Prob. 26ECh. 3.3 - Prob. 27ECh. 3.3 - Prob. 28ECh. 3.3 - Prob. 29ECh. 3.3 - Prob. 30ECh. 3.3 - Prob. 31ECh. 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 - Prob. 40ECh. 3.3 - Prob. 41ECh. 3.3 - Prob. 42ECh. 3.3 - Prob. 43ECh. 3.3 - Find the derivatives of all orders of the...Ch. 3.3 - Prob. 45ECh. 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 - Slopes and Tangent Lines Findall points (x, y) on...Ch. 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 - 75. Suppose that the function in the Derivative...Ch. 3.3 - The Reciprocal Rule The Reciprocal Rule says that...Ch. 3.3 - Generalizing the Product Rule The Derivative...Ch. 3.3 - Prob. 78ECh. 3.3 - Prob. 79ECh. 3.3 - Prob. 80ECh. 3.4 - Motion along a coordinate Line
Exercises 1-6 give...Ch. 3.4 - Prob. 2ECh. 3.4 - Prob. 3ECh. 3.4 - Prob. 4ECh. 3.4 - Prob. 5ECh. 3.4 - Prob. 6ECh. 3.4 - Prob. 7ECh. 3.4 - Prob. 8ECh. 3.4 - Prob. 9ECh. 3.4 - Lunar projectile motion A rock thrown vertically...Ch. 3.4 - Finding g on a small airless planet Explorers on a...Ch. 3.4 - 12. Speeding bullet
A 45- calibre bullet shot...Ch. 3.4 - Prob. 13ECh. 3.4 - Prob. 14ECh. 3.4 - Understanding Motion from Graphs
15. The...Ch. 3.4 - Prob. 16ECh. 3.4 - 17. Launching a rocket
When a model rocket is...Ch. 3.4 - The accompanying figure shows the velocity v=f(t)...Ch. 3.4 - Prob. 19ECh. 3.4 - Prob. 20ECh. 3.4 - Prob. 21ECh. 3.4 - Marginal revenue Suppose that the revenue from...Ch. 3.4 - Prob. 23ECh. 3.4 - Prob. 24ECh. 3.4 - Draining a tank It takes 12 hours to drain a...Ch. 3.4 - Draining a tank The number of gallons of water in...Ch. 3.4 - Vehicular stopping distance Based on data from the...Ch. 3.4 - 28. Inflating a balloon
The volume of a...Ch. 3.4 - 29. Airplane takeoff Suppose that the distance an...Ch. 3.4 - Volcanic lava fountains Although the November 1959...Ch. 3.4 - Exercise 31-34 give the position function of an...Ch. 3.4 - Exercise 31-34 give the position function of an...Ch. 3.4 - Exercise 31-34 give the position function of an...Ch. 3.4 - T Exercise 31-34 give the position function s=f(t)...Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
1.
Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
3.
Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
5.
Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
8.
Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
10.
Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
11.
Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
12.
Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
13.
Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
14.
Ch. 3.5 - Derivatives
In Exercises 1-18, find dy/dx.
15.
Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives In Exercises 1-18, find dy/dx....Ch. 3.5 - Derivatives In Exercises 19-22, find ds/dt....Ch. 3.5 - Derivatives
In Exercises 19-22, find ds/dt.
20.
Ch. 3.5 - Derivatives In Exercises 19-22, find ds/dt....Ch. 3.5 - Derivatives
In Exercises 19-22, find ds/dt.
22.
Ch. 3.5 - Derivatives
In Exercises 23-26, find dr/dθ.
23.
Ch. 3.5 - Derivatives In Exercises 23-26, find dr/d....Ch. 3.5 - Derivatives
In Exercises 23-26, find dr/dθ.
25.
Ch. 3.5 - Derivatives
In Exercises 23-26, find dr/dθ.
26.
Ch. 3.5 - Derivatives
In Exercises 27-32, find dp/dq.
27.
Ch. 3.5 - Derivatives
In Exercises 27-32, find dp/dq.
28.
Ch. 3.5 - Derivatives In Exercises 27-32, find dp/dq....Ch. 3.5 - Derivatives
In Exercises 27-32, find dp/dq.
30.
Ch. 3.5 - Derivatives In Exercises 27-32, find dp/dq....Ch. 3.5 - Derivatives
In Exercises 27-32, find dp/dq.
32.
Ch. 3.5 - Find y if y=cscx. y=secx.Ch. 3.5 - 34. Find
a. b.
Ch. 3.5 - Tangent Lines
In Exercises 35-38, graph the curves...Ch. 3.5 - Tangent Lines
In Exercises 35-38, graph the curves...Ch. 3.5 - Tangent Lines In Exercises 35-38, graph the curves...Ch. 3.5 - Prob. 38ECh. 3.5 - Prob. 39ECh. 3.5 - Prob. 40ECh. 3.5 - Prob. 41ECh. 3.5 - Prob. 42ECh. 3.5 - Prob. 43ECh. 3.5 - Prob. 44ECh. 3.5 - Prob. 45ECh. 3.5 - Tangent Lines Find all points on the curve y=cotx,...Ch. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Prob. 49ECh. 3.5 - Prob. 50ECh. 3.5 - Trigonometric Limits Find the limits in Exercises...Ch. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Prob. 54ECh. 3.5 - Prob. 55ECh. 3.5 - Trigonometric Limits
Find the limits in Exercises...Ch. 3.5 - Prob. 57ECh. 3.5 - Prob. 58ECh. 3.5 - Prob. 59ECh. 3.5 - Is there a value of b that will make...Ch. 3.5 - By computing the first few derivatives and looking...Ch. 3.5 - Prob. 62ECh. 3.5 - A weight is attached to a spring and reaches its...Ch. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 3.5 - Prob. 67ECh. 3.5 - Prob. 68ECh. 3.5 - 69. Slopes on the graph of the tangent function...Ch. 3.5 - Exploring (sinkx)/x Graph y=(sinx)/x, y=(sin2x)/x,...Ch. 3.6 - Prob. 1ECh. 3.6 - Prob. 2ECh. 3.6 - Prob. 3ECh. 3.6 - Prob. 4ECh. 3.6 - Prob. 5ECh. 3.6 - Prob. 6ECh. 3.6 - Prob. 7ECh. 3.6 - Prob. 8ECh. 3.6 - Prob. 9ECh. 3.6 - Prob. 10ECh. 3.6 - Prob. 11ECh. 3.6 - Prob. 12ECh. 3.6 - Prob. 13ECh. 3.6 - Prob. 14ECh. 3.6 - Prob. 15ECh. 3.6 - Prob. 16ECh. 3.6 - Prob. 17ECh. 3.6 - Prob. 18ECh. 3.6 - Prob. 19ECh. 3.6 - Prob. 20ECh. 3.6 - Prob. 21ECh. 3.6 - Prob. 22ECh. 3.6 - Prob. 23ECh. 3.6 - Prob. 24ECh. 3.6 - Prob. 25ECh. 3.6 - Prob. 26ECh. 3.6 - Prob. 27ECh. 3.6 - Prob. 28ECh. 3.6 - Prob. 29ECh. 3.6 - Prob. 30ECh. 3.6 - Prob. 31ECh. 3.6 - Prob. 32ECh. 3.6 - Prob. 33ECh. 3.6 - Prob. 34ECh. 3.6 - Prob. 35ECh. 3.6 - Prob. 36ECh. 3.6 - Prob. 37ECh. 3.6 - Prob. 38ECh. 3.6 - Prob. 39ECh. 3.6 - Prob. 40ECh. 3.6 - Prob. 41ECh. 3.6 - Prob. 42ECh. 3.6 - Prob. 43ECh. 3.6 - Prob. 44ECh. 3.6 - Prob. 45ECh. 3.6 - Prob. 46ECh. 3.6 - Prob. 47ECh. 3.6 - Prob. 48ECh. 3.6 - Prob. 49ECh. 3.6 - Prob. 50ECh. 3.6 - Prob. 51ECh. 3.6 - Prob. 52ECh. 3.6 - Prob. 53ECh. 3.6 - Prob. 54ECh. 3.6 - Prob. 55ECh. 3.6 - Prob. 56ECh. 3.6 - Prob. 57ECh. 3.6 - Prob. 58ECh. 3.6 - Prob. 59ECh. 3.6 - Prob. 60ECh. 3.6 - Prob. 61ECh. 3.6 - Prob. 62ECh. 3.6 - Prob. 63ECh. 3.6 - Prob. 64ECh. 3.6 - Prob. 65ECh. 3.6 - Prob. 66ECh. 3.6 - Prob. 67ECh. 3.6 - Prob. 68ECh. 3.6 - Prob. 69ECh. 3.6 - Prob. 70ECh. 3.6 - Prob. 71ECh. 3.6 - Prob. 72ECh. 3.6 - Prob. 73ECh. 3.6 - Prob. 74ECh. 3.6 - Prob. 75ECh. 3.6 - Prob. 76ECh. 3.6 - Prob. 77ECh. 3.6 - Prob. 78ECh. 3.6 - Prob. 79ECh. 3.6 - Prob. 80ECh. 3.6 - Prob. 81ECh. 3.6 - Prob. 82ECh. 3.6 - Prob. 83ECh. 3.6 - Prob. 84ECh. 3.6 - Prob. 85ECh. 3.6 - Prob. 86ECh. 3.6 - Prob. 87ECh. 3.6 - Prob. 88ECh. 3.6 - Prob. 89ECh. 3.6 - Prob. 90ECh. 3.6 - Prob. 91ECh. 3.6 - Prob. 92ECh. 3.6 - Find dy/dx if y=x by using the Chain Rule with y...Ch. 3.6 - Prob. 94ECh. 3.6 - Prob. 95ECh. 3.6 - Prob. 96ECh. 3.6 - 97.
a. Find the tangent line to the curve at ....Ch. 3.6 - Slopes on sine curves Find equations for the...Ch. 3.6 - Running machinery too fast Suppose that a piston...Ch. 3.6 - Prob. 100ECh. 3.6 - Prob. 101ECh. 3.6 - Constant acceleration Suppose that the velocity of...Ch. 3.6 - Prob. 103ECh. 3.6 - Prob. 104ECh. 3.6 - Prob. 105ECh. 3.6 - Prob. 106ECh. 3.6 - 107. The derivative of
Graph the function for ....Ch. 3.6 - Prob. 108ECh. 3.6 - Prob. 109ECh. 3.6 - Prob. 110ECh. 3.6 - Prob. 111ECh. 3.6 - Prob. 112ECh. 3.6 - Prob. 113ECh. 3.7 - Prob. 1ECh. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Prob. 3ECh. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Use implicit differentiation to find dy/dx in...Ch. 3.7 - Find in Exercises 17-20.
17.
Ch. 3.7 - Find in Exercises 17-20.
18.
Ch. 3.7 - Find dr/d in Exercises 17-20. sin(r)=12Ch. 3.7 - Prob. 20ECh. 3.7 - Second Derivatives In Exercises 21-28, use...Ch. 3.7 - Second Derivatives
In Exercises 21-28, use...Ch. 3.7 - Second Derivatives
In Exercises 21-28, use...Ch. 3.7 - Second Derivatives
In Exercises 21-28, use...Ch. 3.7 - Second Derivatives In Exercises 21-28, use...Ch. 3.7 - Second Derivatives In Exercises 21-28, use...Ch. 3.7 - Second Derivatives In Exercises 21-28, use...Ch. 3.7 - Second Derivatives
In Exercises 21-28, use...Ch. 3.7 - 29. If find the value of at the point (2, 2).
Ch. 3.7 - 30. If find the value of at the point (0, -1).
Ch. 3.7 - In Exercises 31 and 32, find the slope of the...Ch. 3.7 - In Exercises 31 and 32, find the slope of the...Ch. 3.7 - Prob. 33ECh. 3.7 - Slopes, Tangent Lines, and Normal Lines In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines
In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines
In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines
In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines
In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines
In...Ch. 3.7 - Slopes, Tangent Lines, and Normal Lines In...Ch. 3.7 - 43. Parallel tangent lines Find the two points...Ch. 3.7 - 44. Normal lines parallel to a line Find the...Ch. 3.7 - 45. The eight curve Find the slopes of the curve...Ch. 3.7 - The cissoids of Diocles (from about 200 B.C.) Find...Ch. 3.7 - The devils curve (Gabriel Cramer, 1750) Find the...Ch. 3.7 - 48. The folium of Descartes (See Figure 3.29)
a....Ch. 3.7 - 49. Intersecting normal line The line that is...Ch. 3.7 - Power rule for rational exponents Let p and q be...Ch. 3.7 - 51. Normal lines to a parabola Show that if it is...Ch. 3.7 - Is there anything special about the tangent lines...Ch. 3.7 - 53. Verify that the following pairs of curves meet...Ch. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.7 - Prob. 57ECh. 3.7 - Prob. 58ECh. 3.8 - Prob. 1ECh. 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 - Prob. 11ECh. 3.8 - Prob. 12ECh. 3.8 - Prob. 13ECh. 3.8 - Prob. 14ECh. 3.8 - Prob. 15ECh. 3.8 - Prob. 16ECh. 3.8 - Prob. 17ECh. 3.8 - Prob. 18ECh. 3.8 - Prob. 19ECh. 3.8 - Prob. 20ECh. 3.8 - Prob. 21ECh. 3.8 - Prob. 22ECh. 3.8 - Prob. 23ECh. 3.8 - Derivatives of Logarithms In Exercises 11-40, find...Ch. 3.8 - Prob. 25ECh. 3.8 - Prob. 26ECh. 3.8 - Prob. 27ECh. 3.8 - Prob. 28ECh. 3.8 - Prob. 29ECh. 3.8 - Prob. 30ECh. 3.8 - Prob. 31ECh. 3.8 - Prob. 32ECh. 3.8 - Prob. 33ECh. 3.8 - Prob. 34ECh. 3.8 - Prob. 35ECh. 3.8 - Prob. 36ECh. 3.8 - Prob. 37ECh. 3.8 - Prob. 38ECh. 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 - Prob. 48ECh. 3.8 - Prob. 49ECh. 3.8 - Prob. 50ECh. 3.8 - Prob. 51ECh. 3.8 - Prob. 52ECh. 3.8 - Prob. 53ECh. 3.8 - Prob. 54ECh. 3.8 - Prob. 55ECh. 3.8 - Prob. 56ECh. 3.8 - Prob. 57ECh. 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 - Prob. 68ECh. 3.8 - Prob. 69ECh. 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 - Prob. 82ECh. 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 - Prob. 95ECh. 3.8 - Prob. 96ECh. 3.8 - Prob. 97ECh. 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 - Prob. 1ECh. 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 - Prob. 21ECh. 3.9 - Prob. 22ECh. 3.9 - Prob. 23ECh. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Prob. 27ECh. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Prob. 32ECh. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives
In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...Ch. 3.9 - Finding Derivatives In Exercises 21-42, find the...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 - For problems 43-46 use implicit differentiation to...Ch. 3.9 - You are sitting in a classroom next to the wall...Ch. 3.9 - Prob. 48ECh. 3.9 - Here is an informal proof that tan11+tan12+tan13=....Ch. 3.9 - 50. Two derivations of the identity
a....Ch. 3.9 - Which of the expressions in Exercises 51-54 are...Ch. 3.9 - Which of the expressions in Exercises 51-54 are...Ch. 3.9 - Prob. 53ECh. 3.9 - Which of the expressions in Exercises 51-54 are...Ch. 3.9 - 55. Use the identity to derive the formula for the...Ch. 3.9 - Derive the formula dydx=11+x2 for the derivative...Ch. 3.9 - 57. Use the Derivative Rule in Section 3.8,...Ch. 3.9 - 58. Use the identity to derive the formula for the...Ch. 3.9 - What is special about the functions...Ch. 3.9 - What is special about the functions f(x)=sin11x2+1...Ch. 3.9 - T Find the values of sec11.5 csc1(1.5) cot12Ch. 3.9 - 62. Find the values of
b. ...Ch. 3.9 - Prob. 63ECh. 3.9 - Prob. 64ECh. 3.9 - Prob. 65ECh. 3.9 - Prob. 66ECh. 3.9 - Newtons serpentine Graph Newtons serpentine,...Ch. 3.9 - Graph the rational function y=(2x2)/x2. Then graph...Ch. 3.9 - 69. Graph together with its first two...Ch. 3.9 - Graph f(x)=tan1x together with its first two...Ch. 3.10 - 1. Area Suppose that the radius r and area of a...Ch. 3.10 - 2. Surface area Suppose that the radius r and...Ch. 3.10 - Assume that y=5x and dx/dt=2. Find dy/dt.Ch. 3.10 - Assume that 2x+3y=12 and dy/dt=2. Find dx/dt.Ch. 3.10 - 5. If and then what is when ?
Ch. 3.10 - If y=x3y and dy/dt=5, then what is dx/dt when y=2?Ch. 3.10 - Prob. 7ECh. 3.10 - Prob. 8ECh. 3.10 - Prob. 9ECh. 3.10 - Prob. 10ECh. 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 - Prob. 17ECh. 3.10 - Prob. 18ECh. 3.10 - Prob. 19ECh. 3.10 - Prob. 20ECh. 3.10 - Prob. 21ECh. 3.10 - 22. Changing dimensions in a rectangular box...Ch. 3.10 - 23. A sliding ladder A13-ft ladder is leaning...Ch. 3.10 - Prob. 24ECh. 3.10 - Flying a kite A girl flies a kite at a height of...Ch. 3.10 - Prob. 26ECh. 3.10 - 27. A growing sand pile Sand falls from a conveyor...Ch. 3.10 - Prob. 28ECh. 3.10 - Prob. 29ECh. 3.10 - A growing raindrop Suppose that a drop of mist is...Ch. 3.10 - Prob. 31ECh. 3.10 - 32. Hauling in a dinghy A dinghy is pulled toward...Ch. 3.10 - Prob. 33ECh. 3.10 - Making coffee Coffee is draining from a conical...Ch. 3.10 - Prob. 35ECh. 3.10 - 36. Moving along a parabola A particle moves along...Ch. 3.10 - 37. Motion in the plane The coordinates of a...Ch. 3.10 - Videotaping a moving car You are videotaping a...Ch. 3.10 - 39. A moving shadow A light shines from the top of...Ch. 3.10 - A buildings shadow On a morning of a day when the...Ch. 3.10 - Prob. 41ECh. 3.10 - Prob. 42ECh. 3.10 - 43. Baseball players A baseball diamond is a...Ch. 3.10 - Ships Two ships are steaming straight away from a...Ch. 3.10 - Prob. 45ECh. 3.10 - 46. Oil spill An explosion at an oil rig located...Ch. 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 - Common linear approximations at x=0 Find the...Ch. 3.11 - Prob. 7ECh. 3.11 - Prob. 8ECh. 3.11 - Prob. 9ECh. 3.11 - Prob. 10ECh. 3.11 - In Exercises 7-14, find a linearization at a...Ch. 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 - 52. The diameter of a tree was During the...Ch. 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 - 63. Unclogging arteries The formula , discovered...Ch. 3.11 - Prob. 64ECh. 3.11 - Prob. 65ECh. 3.11 - Prob. 66ECh. 3.11 - Prob. 67ECh. 3.11 - Prob. 68ECh. 3 - Prob. 1GYRCh. 3 - Prob. 2GYRCh. 3 - Prob. 3GYRCh. 3 - Prob. 4GYRCh. 3 - Prob. 5GYRCh. 3 - Prob. 6GYRCh. 3 - 7. How is a function’s differentiability at a...Ch. 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 - 17. What do the limits and have to do with the...Ch. 3 - Prob. 18GYRCh. 3 - Prob. 19GYRCh. 3 - 20. What is the rule for calculating the...Ch. 3 - Prob. 21GYRCh. 3 - Prob. 22GYRCh. 3 - Prob. 23GYRCh. 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 - If x moves from a to a nearby value a + dx, how do...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Prob. 3PECh. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Prob. 9PECh. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Prob. 17PECh. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions Find the derivatives of...Ch. 3 - Derivatives of Functions
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Find the derivatives of...Ch. 3 - Derivatives of Functions
Find the derivatives of...Ch. 3 - Prob. 52PECh. 3 - Prob. 53PECh. 3 - Prob. 54PECh. 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 - Implicit Differentiation In Exercises 65-78, find...Ch. 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 - Prob. 81PECh. 3 - Prob. 82PECh. 3 - Prob. 83PECh. 3 - Prob. 84PECh. 3 - Numerical Values of Derivatives Suppose that...Ch. 3 - Numerical Values of Derivatives
86. Suppose that...Ch. 3 - Prob. 87PECh. 3 - Prob. 88PECh. 3 - Prob. 89PECh. 3 - Numerical Values of Derivatives Find the value of...Ch. 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 - 104. Intersecting tangent lines Show that the...Ch. 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 - Show how to extend the functions in Exercises 131...Ch. 3 - Prob. 133PECh. 3 - Prob. 134PECh. 3 - Prob. 135PECh. 3 - Prob. 136PECh. 3 - Prob. 137PECh. 3 - Prob. 138PECh. 3 - 139. Right circular cylinder The total surface...Ch. 3 - 140. Right circular cone The lateral surface area...Ch. 3 - Circles changing area The radius r of a circle is...Ch. 3 - Cubes changing edges The volume of a cube is...Ch. 3 - Resistors connected in parallel If two resistors...Ch. 3 - 144. Impedance in a series circuit The impedance...Ch. 3 - Speed of moving particle The coordinates of a...Ch. 3 - 146. Motion of a particle A particle moves along...Ch. 3 - 147. Draining a tank Water drains from the conical...Ch. 3 - Rotating spool Astelevision cable is pulled from a...Ch. 3 - Moving searchlight beam The figure shows a boat 1...Ch. 3 - Points moving on coordinate axes Points A and B...Ch. 3 - 151. Find the linearizations of
a. at .
b. at...Ch. 3 - 152. We can obtain a useful linear approximation...Ch. 3 - 153. Find the linearization of at.
Ch. 3 - Find the linearization of f(x)=2/(1x)+1+x3.1 at...Ch. 3 - 155. Surface area of a cone Write a formula that...Ch. 3 - Prob. 156PECh. 3 - Compounding error The circumference of the equator...Ch. 3 - Prob. 158PECh. 3 - An equation like sin2+cos2=1 is called an identity...Ch. 3 - If the identity sin(x+a)=sinxscosa+cosxsina is...Ch. 3 - 3. a. Find values for the constants that will make...Ch. 3 - Solutions to differential equations Show that...Ch. 3 - 5. An osculating circle Find the values of and...Ch. 3 - Prob. 6AAECh. 3 - Industrial production Economists often use the...Ch. 3 - Designing a gondola The designer of a...Ch. 3 - 9. Pisa by parachute On August 5, 1988, Mike...Ch. 3 - Motion of a particle The position at time t0 of a...Ch. 3 - 11. Shooting a paper clip On Earth, you can easily...Ch. 3 - Prob. 12AAECh. 3 - Prob. 13AAECh. 3 - In Exercises 14 and 15, use implicit...Ch. 3 - Prob. 15AAECh. 3 - 16. Average and instantaneous velocity
a. Show...Ch. 3 - Find all values of the constants m and b for which...Ch. 3 - Does the function f(x)={1cosxx,x00,x=0 have a...Ch. 3 - 19. a. For what values of and will
be...Ch. 3 - For what values of a and b will...Ch. 3 - Odd differentiable functions Is there anything...Ch. 3 - Even differentiable functions Is there anything...Ch. 3 - Suppose that the functions f and g are defined...Ch. 3 - (Continuation of Exercise 23.) Use the result of...Ch. 3 - Is the derivative of h(x)={x2sin(1/x),x00,x=0...Ch. 3 - Prob. 29AAECh. 3 - Leibnizs rule for higher-order derivatives of...Ch. 3 - The period of a clock pendulum The period T of a...
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