University Calculus: Early Transcendentals, Single Variable (3rd Edition)
3rd Edition
ISBN: 9780321999634
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 3.5, Problem 57E
To determine
To calculate: Whether there is avalue of
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Suppose an oil spill covers a circular area and the radius, r, increases according to the graph shown below where t
represents the number of minutes since the spill was first observed.
Radius (feet)
80
70
60
50
40
30
20
10
0
r
0 10 20 30 40 50 60 70 80 90
Time (minutes)
(a) How large is the circular area of the spill 30 minutes after it was first observed? Give your answer in terms of π.
square feet
(b) If the cost to clean the oil spill is proportional to the square of the diameter of the spill, express the cost, C, as a
function of the radius of the spill, r. Use a lower case k as the proportionality constant.
C(r) =
(c) Which of the following expressions could be used to represent the amount of time it took for the radius of the spill to
increase from 20 feet to 60 feet?
r(60) - r(20)
Or¹(80-30)
r(80) - r(30)
r-1(80) - r−1(30)
r-1(60) - r¹(20)
6. Graph the function f(x)=log3x. Label three points on the graph (one should be the intercept) with
corresponding ordered pairs and label the asymptote with its equation. Write the domain and range of the function
in interval notation. Make your graph big enough to see all important features.
Find the average value gave of the function g on the given interval.
gave =
g(x) = 8√√x, [8,64]
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Chapter 3 Solutions
University Calculus: Early Transcendentals, Single Variable (3rd Edition)
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. 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. 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 - 57. Derivative of Does knowing that function is...Ch. 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 - 64. Weierstrass’s nowhere differentiable...Ch. 3.2 - Prob. 63ECh. 3.2 - Prob. 64ECh. 3.2 - Prob. 67ECh. 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 - 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. 76ECh. 3.3 - Prob. 77ECh. 3.3 - Prob. 78ECh. 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. 21ECh. 3.4 - Prob. 22ECh. 3.4 - Prob. 23ECh. 3.4 - Marginal revenue Suppose that the revenue from...Ch. 3.4 - Prob. 25ECh. 3.4 - Prob. 26ECh. 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 - Tangent Lines Find all points on the curve y=cotx,...Ch. 3.5 - Prob. 45ECh. 3.5 - Prob. 46ECh. 3.5 - Prob. 47ECh. 3.5 - Prob. 48ECh. 3.5 - Trigonometric Limits Find the limits in Exercises...Ch. 3.5 - Prob. 50ECh. 3.5 - Prob. 51ECh. 3.5 - Prob. 52ECh. 3.5 - Prob. 53ECh. 3.5 - Trigonometric Limits
Find the limits in Exercises...Ch. 3.5 - Prob. 55ECh. 3.5 - Prob. 56ECh. 3.5 - Prob. 57ECh. 3.5 - Is there a value of b that will make...Ch. 3.5 - Prob. 60ECh. 3.5 - A weight is attached to a spring and reaches its...Ch. 3.5 - Prob. 62ECh. 3.5 - Prob. 63ECh. 3.5 - Prob. 64ECh. 3.5 - Prob. 65ECh. 3.5 - Prob. 66ECh. 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 - Find dy/dx if y=x by using the Chain Rule with y...Ch. 3.6 - Prob. 92ECh. 3.6 - Prob. 93ECh. 3.6 - Prob. 94ECh. 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. 98ECh. 3.6 - Prob. 99ECh. 3.6 - Constant acceleration Suppose that the velocity of...Ch. 3.6 - Prob. 101ECh. 3.6 - Prob. 102ECh. 3.6 - Prob. 103ECh. 3.6 - Prob. 104ECh. 3.6 - 107. The derivative of
Graph the function for ....Ch. 3.6 - Prob. 106ECh. 3.6 - Prob. 107ECh. 3.6 - Prob. 108ECh. 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 - 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. 31ECh. 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. 52ECh. 3.7 - Prob. 53ECh. 3.7 - Prob. 54ECh. 3.7 - Prob. 55ECh. 3.7 - Prob. 56ECh. 3.8 - Prob. 1ECh. 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. 3.9 - 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 - You are sitting in a classroom next to the wall...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. 47ECh. 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 - Prob. 55ECh. 3.9 - Prob. 56ECh. 3.9 - Prob. 57ECh. 3.9 - Prob. 58ECh. 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. 3.11 - 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 - 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. 154PECh. 3 - Compounding error The circumference of the equator...Ch. 3 - Prob. 156PECh. 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 - 5. An osculating circle Find the values of and...Ch. 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. 10AAECh. 3 - Prob. 11AAECh. 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 - Leibnizs rule for higher-order derivatives of...Ch. 3 - The period of a clock pendulum The period T of a...
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