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

Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
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Question
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Chapter 4.3, Problem 1E

(a)

To determine

Find the critical points function f.

(b)

To determine

Find the increasing and decreasing open interval of f.

(c)

To determine

Find the local maximum and local minimum of function f.

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Chapter 4 Solutions

University Calculus: Early Transcendentals (4th Edition)

Ch. 4.1 - In Exercises 16, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 3ECh. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 5ECh. 4.1 - Prob. 6ECh. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 9ECh. 4.1 - Prob. 10E
Ch. 4.1 - Prob. 11ECh. 4.1 - In Exercises 11–14, match the table with a...Ch. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - In Exercises 15–20, sketch the graph of each...Ch. 4.1 - In Exercises 15-20, sketch the graph of each...Ch. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - In Exercises 15–20, sketch the graph of each...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - Prob. 29ECh. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - In Exercises 37-40: Find the absolute maximum and...Ch. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - In Exercises 41–44, find the function’s absolute...Ch. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - Prob. 55ECh. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - Prob. 62ECh. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Cubic functions Consider the cubic function Show...Ch. 4.1 - Prob. 69ECh. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Prob. 2ECh. 4.2 - Prob. 3ECh. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Prob. 5ECh. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Prob. 7ECh. 4.2 - Prob. 8ECh. 4.2 - Prob. 9ECh. 4.2 - Prob. 10ECh. 4.2 - Which of the functions in Exercises 9–14 satisfy...Ch. 4.2 - Prob. 12ECh. 4.2 - Prob. 13ECh. 4.2 - Prob. 14ECh. 4.2 - Prob. 15ECh. 4.2 - Prob. 16ECh. 4.2 - Prob. 17ECh. 4.2 - Prob. 18ECh. 4.2 - Prob. 19ECh. 4.2 - Prob. 20ECh. 4.2 - Show that the functions in Exercises 21–28 have...Ch. 4.2 - Show that the functions in Exercises 21–28 have...Ch. 4.2 - Prob. 23ECh. 4.2 - Prob. 24ECh. 4.2 - Prob. 25ECh. 4.2 - Prob. 26ECh. 4.2 - Prob. 27ECh. 4.2 - Show that the functions in Exercises 21–28 have...Ch. 4.2 - Prob. 29ECh. 4.2 - Prob. 30ECh. 4.2 - Prob. 31ECh. 4.2 - Prob. 32ECh. 4.2 - Prob. 33ECh. 4.2 - Prob. 34ECh. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - Prob. 38ECh. 4.2 - Prob. 39ECh. 4.2 - Prob. 40ECh. 4.2 - In Exercises 39–42, find the function with the...Ch. 4.2 - Prob. 42ECh. 4.2 - Prob. 43ECh. 4.2 - Prob. 44ECh. 4.2 - Prob. 45ECh. 4.2 - Prob. 46ECh. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Prob. 50ECh. 4.2 - Prob. 51ECh. 4.2 - Prob. 52ECh. 4.2 - Prob. 53ECh. 4.2 - Prob. 54ECh. 4.2 - Prob. 55ECh. 4.2 - Prob. 56ECh. 4.2 - Prob. 57ECh. 4.2 - Prob. 58ECh. 4.2 - Prob. 59ECh. 4.2 - Prob. 60ECh. 4.2 - Prob. 61ECh. 4.2 - Prob. 62ECh. 4.2 - Prob. 63ECh. 4.2 - Prob. 64ECh. 4.2 - Prob. 65ECh. 4.2 - Prob. 66ECh. 4.2 - Prob. 67ECh. 4.2 - Prob. 68ECh. 4.2 - Prob. 69ECh. 4.2 - Prob. 70ECh. 4.2 - Prob. 71ECh. 4.2 - Prob. 72ECh. 4.2 - Prob. 73ECh. 4.2 - Prob. 74ECh. 4.2 - Prob. 75ECh. 4.2 - Prob. 76ECh. 4.2 - Prob. 77ECh. 4.2 - Prob. 78ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 2ECh. 4.3 - Prob. 3ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 5ECh. 4.3 - Prob. 6ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 9ECh. 4.3 - Prob. 10ECh. 4.3 - Prob. 11ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 13ECh. 4.3 - Prob. 14ECh. 4.3 - Prob. 15ECh. 4.3 - In Exercises 15–18: Find the open intervals on...Ch. 4.3 - Prob. 17ECh. 4.3 - Prob. 18ECh. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 21ECh. 4.3 - Prob. 22ECh. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 26ECh. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 29ECh. 4.3 - Prob. 30ECh. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 34ECh. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 37ECh. 4.3 - Prob. 38ECh. 4.3 - Prob. 39ECh. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - Prob. 41ECh. 4.3 - Prob. 42ECh. 4.3 - Prob. 43ECh. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Prob. 45ECh. 4.3 - Prob. 46ECh. 4.3 - Prob. 47ECh. 4.3 - Prob. 48ECh. 4.3 - In Exercises 47–58: Identify the function’s local...Ch. 4.3 - Prob. 50ECh. 4.3 - Prob. 51ECh. 4.3 - Prob. 52ECh. 4.3 - Prob. 53ECh. 4.3 - Prob. 54ECh. 4.3 - In Exercises 47–58: Identify the function’s local...Ch. 4.3 - In Exercises 47–58: Identify the function’s local...Ch. 4.3 - Prob. 57ECh. 4.3 - Prob. 58ECh. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - Prob. 61ECh. 4.3 - Prob. 62ECh. 4.3 - Prob. 63ECh. 4.3 - In Exercises 59–66: Find the local extrema of each...Ch. 4.3 - Prob. 65ECh. 4.3 - Prob. 66ECh. 4.3 - In Exercises 67 and 68, the graph of f′ is given....Ch. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Sketch the graph of a differentiable function y =...Ch. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Prob. 77ECh. 4.3 - Prob. 78ECh. 4.3 - Prob. 79ECh. 4.3 - Prob. 80ECh. 4.3 - Prob. 81ECh. 4.3 - Prob. 82ECh. 4.3 - Prob. 83ECh. 4.3 - Prob. 84ECh. 4.3 - Prob. 85ECh. 4.3 - Prob. 86ECh. 4.3 - Prob. 87ECh. 4.3 - Prob. 88ECh. 4.3 - Prob. 89ECh. 4.3 - Prob. 90ECh. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Prob. 2ECh. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Prob. 6ECh. 4.4 - Prob. 7ECh. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Prob. 9ECh. 4.4 - Prob. 10ECh. 4.4 - Prob. 11ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 14ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 16ECh. 4.4 - Prob. 17ECh. 4.4 - Prob. 18ECh. 4.4 - Prob. 19ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 22ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 24ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 29ECh. 4.4 - Prob. 30ECh. 4.4 - Prob. 31ECh. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - Prob. 34ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - Prob. 38ECh. 4.4 - Prob. 39ECh. 4.4 - Prob. 40ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 42ECh. 4.4 - Prob. 43ECh. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - Prob. 49ECh. 4.4 - Prob. 50ECh. 4.4 - Prob. 51ECh. 4.4 - Prob. 52ECh. 4.4 - Prob. 53ECh. 4.4 - Prob. 54ECh. 4.4 - Prob. 55ECh. 4.4 - Prob. 56ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 58ECh. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Prob. 64ECh. 4.4 - Prob. 65ECh. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - In Exercises 9–70, graph the function using...Ch. 4.4 - Prob. 70ECh. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 4.4 - Prob. 72ECh. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 4.4 - Prob. 74ECh. 4.4 - Prob. 75ECh. 4.4 - Prob. 76ECh. 4.4 - Prob. 77ECh. 4.4 - Prob. 78ECh. 4.4 - Prob. 79ECh. 4.4 - Prob. 80ECh. 4.4 - Prob. 81ECh. 4.4 - Prob. 82ECh. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Prob. 85ECh. 4.4 - Prob. 86ECh. 4.4 - Prob. 87ECh. 4.4 - Prob. 88ECh. 4.4 - Prob. 89ECh. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Each of Exercises 93–96 shows the graphs of the...Ch. 4.4 - Prob. 94ECh. 4.4 - Each of Exercises 93–96 shows the graphs of the...Ch. 4.4 - Prob. 96ECh. 4.4 - The accompanying figure shows a portion of the...Ch. 4.4 - Prob. 98ECh. 4.4 - Sketch the graph of a twice-differentiable...Ch. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Prob. 102ECh. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Prob. 105ECh. 4.4 - In Exercises 105 and 106, the graph of f′ is...Ch. 4.4 - Motion Along a Line The graphs in Exercises 107...Ch. 4.4 - Prob. 108ECh. 4.4 - Prob. 109ECh. 4.4 - Prob. 110ECh. 4.4 - Prob. 111ECh. 4.4 - Prob. 112ECh. 4.4 - Prob. 113ECh. 4.4 - Prob. 114ECh. 4.4 - Prob. 115ECh. 4.4 - Prob. 116ECh. 4.4 - Prob. 117ECh. 4.4 - Prob. 118ECh. 4.4 - Prob. 119ECh. 4.4 - Prob. 120ECh. 4.4 - Prob. 121ECh. 4.4 - Prob. 122ECh. 4.4 - Prob. 127ECh. 4.4 - Prob. 128ECh. 4.5 - In Exercises 16, use l’Hôpital’s Rule to evaluate...Ch. 4.5 - In Exercises 1–6, use l’Hôpital’s Rule to evaluate...Ch. 4.5 - In Exercises 1–6, use l’Hôpital’s Rule to evaluate...Ch. 4.5 - Prob. 4ECh. 4.5 - Prob. 5ECh. 4.5 - Prob. 6ECh. 4.5 - Prob. 7ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 9ECh. 4.5 - Prob. 10ECh. 4.5 - Prob. 11ECh. 4.5 - Prob. 12ECh. 4.5 - Prob. 13ECh. 4.5 - Prob. 14ECh. 4.5 - Prob. 15ECh. 4.5 - Prob. 16ECh. 4.5 - Prob. 17ECh. 4.5 - Prob. 18ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 20ECh. 4.5 - Prob. 21ECh. 4.5 - Prob. 22ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 24ECh. 4.5 - Prob. 25ECh. 4.5 - Prob. 26ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 28ECh. 4.5 - Prob. 29ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 31ECh. 4.5 - Prob. 32ECh. 4.5 - Prob. 33ECh. 4.5 - Prob. 34ECh. 4.5 - Prob. 35ECh. 4.5 - Prob. 36ECh. 4.5 - Prob. 37ECh. 4.5 - Prob. 38ECh. 4.5 - Prob. 39ECh. 4.5 - Use 1’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 41ECh. 4.5 - Prob. 42ECh. 4.5 - Prob. 43ECh. 4.5 - Prob. 44ECh. 4.5 - Prob. 45ECh. 4.5 - Prob. 46ECh. 4.5 - Prob. 47ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 49ECh. 4.5 - Prob. 50ECh. 4.5 - Prob. 51ECh. 4.5 - Prob. 52ECh. 4.5 - Prob. 53ECh. 4.5 - Prob. 54ECh. 4.5 - Prob. 55ECh. 4.5 - Prob. 56ECh. 4.5 - Prob. 57ECh. 4.5 - Prob. 58ECh. 4.5 - Prob. 59ECh. 4.5 - Prob. 60ECh. 4.5 - Find the limits in Exercises 51–66. 61. Ch. 4.5 - Prob. 62ECh. 4.5 - Prob. 63ECh. 4.5 - Prob. 64ECh. 4.5 - Prob. 65ECh. 4.5 - Prob. 66ECh. 4.5 - Prob. 67ECh. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - Prob. 70ECh. 4.5 - Prob. 71ECh. 4.5 - Prob. 72ECh. 4.5 - L’Hôpital’s Rule does not help with the limits in...Ch. 4.5 - Prob. 74ECh. 4.5 - Prob. 75ECh. 4.5 - Prob. 76ECh. 4.5 - Prob. 77ECh. 4.5 - Prob. 78ECh. 4.5 - Prob. 79ECh. 4.5 - Prob. 80ECh. 4.5 - Prob. 81ECh. 4.5 - Prob. 82ECh. 4.5 - Prob. 83ECh. 4.5 - Prob. 84ECh. 4.5 - Prob. 85ECh. 4.5 - Prob. 86ECh. 4.5 - Prob. 87ECh. 4.5 - Find f′(0) for Ch. 4.5 - Prob. 89ECh. 4.5 - Prob. 90ECh. 4.6 - Minimizing perimeter What is the smallest...Ch. 4.6 - Show that among all rectangles with an 8-m...Ch. 4.6 - The figure shows a rectangle inscribed in an...Ch. 4.6 - A rectangle has its base on the x-axis and its...Ch. 4.6 - You are planning to make an open rectangular box...Ch. 4.6 - You are planning to close off a corner of the...Ch. 4.6 - The best fencing plan A rectangular plot of...Ch. 4.6 - The shortest fence A 216 m2 rectangular pea patch...Ch. 4.6 - Prob. 9ECh. 4.6 - Prob. 10ECh. 4.6 - Designing a poster You are designing a rectangular...Ch. 4.6 - Prob. 12ECh. 4.6 - Two sides of a triangle have lengths a and b, and...Ch. 4.6 - Prob. 14ECh. 4.6 - Designing a can You are designing a 1000 cm3 right...Ch. 4.6 - Prob. 16ECh. 4.6 - Prob. 17ECh. 4.6 - Prob. 18ECh. 4.6 - Find the dimensions of a right circular cylinder...Ch. 4.6 - The U.S. Postal Service will accept a box for...Ch. 4.6 - Prob. 21ECh. 4.6 - Prob. 22ECh. 4.6 - A silo (base not included) is to be constructed in...Ch. 4.6 - The trough in the figure is to be made to the...Ch. 4.6 - Prob. 25ECh. 4.6 - Prob. 26ECh. 4.6 - Constructing cones A right triangle whose...Ch. 4.6 - Prob. 28ECh. 4.6 - Prob. 29ECh. 4.6 - Prob. 30ECh. 4.6 - Prob. 31ECh. 4.6 - Prob. 32ECh. 4.6 - Determine the dimensions of the rectangle of...Ch. 4.6 - Prob. 34ECh. 4.6 - Prob. 35ECh. 4.6 - What values of a and b make f(x) = x3+ ax2 + bx...Ch. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Prob. 39ECh. 4.6 - Find the point on the graph of y = 20x3 + 60x −...Ch. 4.6 - Prob. 41ECh. 4.6 - Prob. 42ECh. 4.6 - Prob. 43ECh. 4.6 - Quickest route Jane is 2 mi offshore in a boat and...Ch. 4.6 - Prob. 45ECh. 4.6 - Prob. 46ECh. 4.6 - Prob. 47ECh. 4.6 - Projectile motion The range R of a projectile...Ch. 4.6 - Prob. 49ECh. 4.6 - Prob. 50ECh. 4.6 - Prob. 51ECh. 4.6 - Two masses hanging side by side from springs have...Ch. 4.6 - Prob. 53ECh. 4.6 - Prob. 54ECh. 4.6 - Prob. 55ECh. 4.6 - Airplane landing path An airplane is flying at...Ch. 4.6 - Prob. 57ECh. 4.6 - Prob. 58ECh. 4.6 - Wilson lot size formula One of the formulas for...Ch. 4.6 - Prob. 60ECh. 4.6 - Prob. 61ECh. 4.6 - Prob. 62ECh. 4.6 - You are to construct an open rectangular box with...Ch. 4.6 - Prob. 64ECh. 4.6 - Sensitivity to medicine (Continuation of Exercise...Ch. 4.6 - How we cough When we cough, the trachea (windpipe)...Ch. 4.6 - Prob. 67ECh. 4.6 - The derivative dt/dx in Example 4 Show that is an...Ch. 4.6 - Prob. 69ECh. 4.6 - Prob. 70ECh. 4.6 - Prob. 71ECh. 4.6 - Prob. 72ECh. 4.6 - Prob. 73ECh. 4.6 - Prob. 74ECh. 4.7 - Use Newton’s method to estimate the solutions of...Ch. 4.7 - Use Newton’s method to estimate the one real...Ch. 4.7 - Prob. 3ECh. 4.7 - Prob. 4ECh. 4.7 - Prob. 5ECh. 4.7 - Prob. 6ECh. 4.7 - Prob. 7ECh. 4.7 - Prob. 8ECh. 4.7 - Prob. 9ECh. 4.7 - Prob. 10ECh. 4.7 - Prob. 11ECh. 4.7 - Prob. 12ECh. 4.7 - Prob. 13ECh. 4.7 - Prob. 14ECh. 4.7 - Prob. 15ECh. 4.7 - Prob. 16ECh. 4.7 - Prob. 17ECh. 4.7 - Prob. 18ECh. 4.7 - Prob. 19ECh. 4.7 - Prob. 20ECh. 4.7 - Prob. 21ECh. 4.7 - Prob. 22ECh. 4.7 - Prob. 23ECh. 4.7 - Prob. 24ECh. 4.7 - Prob. 25ECh. 4.7 - Prob. 26ECh. 4.7 - Intersection of curves At what value(s) of x does ...Ch. 4.7 - Prob. 28ECh. 4.7 - Prob. 29ECh. 4.7 - Prob. 30ECh. 4.7 - Prob. 31ECh. 4.7 - Prob. 32ECh. 4.7 - Prob. 33ECh. 4.7 - Prob. 34ECh. 4.8 - In Exercises 124, find an antiderivative for each...Ch. 4.8 - Prob. 2ECh. 4.8 - Prob. 3ECh. 4.8 - Prob. 4ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 8ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 10ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 12ECh. 4.8 - Prob. 13ECh. 4.8 - Prob. 14ECh. 4.8 - Prob. 15ECh. 4.8 - Prob. 16ECh. 4.8 - Prob. 17ECh. 4.8 - Prob. 18ECh. 4.8 - Prob. 19ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 21ECh. 4.8 - Prob. 22ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 24ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 28ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 30ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 32ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 34ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 36ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 38ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 42ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 44ECh. 4.8 - Prob. 45ECh. 4.8 - Prob. 46ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 48ECh. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 50ECh. 4.8 - Prob. 51ECh. 4.8 - Prob. 52ECh. 4.8 - Prob. 53ECh. 4.8 - Prob. 54ECh. 4.8 - In Exercises 25-70, find the most general...Ch. 4.8 - Prob. 56ECh. 4.8 - Prob. 57ECh. 4.8 - Prob. 58ECh. 4.8 - Prob. 59ECh. 4.8 - Prob. 60ECh. 4.8 - In Exercises 25-70, find the most general...Ch. 4.8 - Prob. 62ECh. 4.8 - Prob. 63ECh. 4.8 - Prob. 64ECh. 4.8 - Prob. 65ECh. 4.8 - Prob. 66ECh. 4.8 - Prob. 67ECh. 4.8 - Prob. 68ECh. 4.8 - Prob. 69ECh. 4.8 - Prob. 70ECh. 4.8 - Prob. 71ECh. 4.8 - Prob. 72ECh. 4.8 - Prob. 73ECh. 4.8 - Prob. 74ECh. 4.8 - Prob. 75ECh. 4.8 - Prob. 76ECh. 4.8 - Prob. 77ECh. 4.8 - Prob. 78ECh. 4.8 - Prob. 79ECh. 4.8 - Prob. 80ECh. 4.8 - Prob. 81ECh. 4.8 - Prob. 82ECh. 4.8 - Prob. 83ECh. 4.8 - Prob. 84ECh. 4.8 - Prob. 85ECh. 4.8 - Prob. 86ECh. 4.8 - Prob. 87ECh. 4.8 - Prob. 88ECh. 4.8 - Prob. 89ECh. 4.8 - Prob. 90ECh. 4.8 - Prob. 91ECh. 4.8 - Prob. 92ECh. 4.8 - Prob. 93ECh. 4.8 - Prob. 94ECh. 4.8 - Prob. 95ECh. 4.8 - Prob. 96ECh. 4.8 - Prob. 97ECh. 4.8 - Prob. 98ECh. 4.8 - Prob. 99ECh. 4.8 - Prob. 100ECh. 4.8 - Prob. 101ECh. 4.8 - Prob. 102ECh. 4.8 - Prob. 103ECh. 4.8 - Prob. 104ECh. 4.8 - Prob. 105ECh. 4.8 - Prob. 106ECh. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Prob. 108ECh. 4.8 - Prob. 109ECh. 4.8 - Prob. 110ECh. 4.8 - Prob. 111ECh. 4.8 - Prob. 112ECh. 4.8 - Prob. 113ECh. 4.8 - Prob. 114ECh. 4.8 - Prob. 115ECh. 4.8 - Prob. 116ECh. 4.8 - Prob. 117ECh. 4.8 - Prob. 118ECh. 4.8 - Prob. 119ECh. 4.8 - Prob. 120ECh. 4.8 - Prob. 121ECh. 4.8 - Prob. 122ECh. 4.8 - Prob. 123ECh. 4.8 - Prob. 124ECh. 4.8 - Prob. 125ECh. 4.8 - Prob. 126ECh. 4.8 - Prob. 127ECh. 4.8 - Prob. 128ECh. 4.8 - Prob. 129ECh. 4.8 - Prob. 130ECh. 4.8 - Prob. 131ECh. 4 - Prob. 1GYRCh. 4 - Prob. 2GYRCh. 4 - Prob. 3GYRCh. 4 - Prob. 4GYRCh. 4 - Prob. 5GYRCh. 4 - Prob. 6GYRCh. 4 - Prob. 7GYRCh. 4 - Prob. 8GYRCh. 4 - Prob. 9GYRCh. 4 - Prob. 10GYRCh. 4 - Prob. 11GYRCh. 4 - Prob. 12GYRCh. 4 - Prob. 13GYRCh. 4 - Prob. 14GYRCh. 4 - Prob. 15GYRCh. 4 - Prob. 16GYRCh. 4 - Prob. 17GYRCh. 4 - Prob. 18GYRCh. 4 - Prob. 19GYRCh. 4 - Prob. 20GYRCh. 4 - Prob. 21GYRCh. 4 - Prob. 22GYRCh. 4 - Prob. 23GYRCh. 4 - Prob. 24GYRCh. 4 - Prob. 25GYRCh. 4 - Prob. 1PECh. 4 - Prob. 2PECh. 4 - Prob. 3PECh. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - Prob. 7PECh. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - Prob. 11PECh. 4 - Prob. 12PECh. 4 - Prob. 13PECh. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Prob. 17PECh. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - Prob. 23PECh. 4 - Prob. 24PECh. 4 - Prob. 25PECh. 4 - Prob. 26PECh. 4 - Prob. 27PECh. 4 - Prob. 28PECh. 4 - Prob. 29PECh. 4 - Prob. 30PECh. 4 - Prob. 31PECh. 4 - Prob. 32PECh. 4 - Prob. 33PECh. 4 - Prob. 34PECh. 4 - Prob. 35PECh. 4 - Prob. 36PECh. 4 - Prob. 37PECh. 4 - Prob. 38PECh. 4 - Prob. 39PECh. 4 - Prob. 40PECh. 4 - Prob. 41PECh. 4 - Prob. 42PECh. 4 - Prob. 43PECh. 4 - Prob. 44PECh. 4 - Prob. 45PECh. 4 - Prob. 46PECh. 4 - Prob. 47PECh. 4 - Prob. 48PECh. 4 - Prob. 49PECh. 4 - Prob. 50PECh. 4 - Prob. 51PECh. 4 - Prob. 52PECh. 4 - Prob. 53PECh. 4 - Prob. 54PECh. 4 - Graph the curves in Exercises 43–58. 55. y = ln...Ch. 4 - Prob. 56PECh. 4 - Prob. 57PECh. 4 - Prob. 58PECh. 4 - Prob. 59PECh. 4 - Prob. 60PECh. 4 - Prob. 61PECh. 4 - Prob. 62PECh. 4 - Prob. 63PECh. 4 - Prob. 64PECh. 4 - Prob. 65PECh. 4 - Prob. 66PECh. 4 - Prob. 67PECh. 4 - Prob. 68PECh. 4 - Prob. 69PECh. 4 - Prob. 70PECh. 4 - Prob. 71PECh. 4 - Prob. 72PECh. 4 - Prob. 73PECh. 4 - Prob. 74PECh. 4 - Prob. 75PECh. 4 - Prob. 76PECh. 4 - Prob. 77PECh. 4 - Prob. 78PECh. 4 - Prob. 79PECh. 4 - Prob. 80PECh. 4 - Prob. 81PECh. 4 - Prob. 82PECh. 4 - Prob. 83PECh. 4 - Prob. 84PECh. 4 - Prob. 85PECh. 4 - Prob. 86PECh. 4 - Use l’Hôpital’s Rule to find the limits in...Ch. 4 - Prob. 88PECh. 4 - Prob. 89PECh. 4 - Prob. 90PECh. 4 - Prob. 91PECh. 4 - Prob. 92PECh. 4 - Prob. 93PECh. 4 - Prob. 94PECh. 4 - Prob. 95PECh. 4 - Prob. 96PECh. 4 - Prob. 97PECh. 4 - Prob. 98PECh. 4 - Prob. 99PECh. 4 - Prob. 100PECh. 4 - Prob. 101PECh. 4 - Prob. 102PECh. 4 - Prob. 103PECh. 4 - Prob. 104PECh. 4 - Prob. 105PECh. 4 - Prob. 106PECh. 4 - Prob. 107PECh. 4 - Prob. 108PECh. 4 - Prob. 109PECh. 4 - Prob. 110PECh. 4 - Prob. 111PECh. 4 - Prob. 112PECh. 4 - Prob. 113PECh. 4 - Prob. 114PECh. 4 - Prob. 115PECh. 4 - Prob. 116PECh. 4 - Prob. 117PECh. 4 - Prob. 118PECh. 4 - Prob. 119PECh. 4 - Prob. 120PECh. 4 - Prob. 121PECh. 4 - Prob. 122PECh. 4 - Prob. 123PECh. 4 - Prob. 124PECh. 4 - Prob. 125PECh. 4 - Prob. 126PECh. 4 - Prob. 127PECh. 4 - Prob. 128PECh. 4 - Prob. 129PECh. 4 - Prob. 130PECh. 4 - Prob. 131PECh. 4 - Prob. 132PECh. 4 - Prob. 133PECh. 4 - Prob. 134PECh. 4 - Prob. 135PECh. 4 - Prob. 136PECh. 4 - Prob. 137PECh. 4 - Prob. 138PECh. 4 - Prob. 139PECh. 4 - Prob. 140PECh. 4 - Prob. 141PECh. 4 - Prob. 142PECh. 4 - Prob. 143PECh. 4 - Prob. 144PECh. 4 - Prob. 145PECh. 4 - Prob. 146PECh. 4 - Prob. 147PECh. 4 - Prob. 148PECh. 4 - Prob. 149PECh. 4 - Prob. 150PECh. 4 - Prob. 151PECh. 4 - Prob. 152PECh. 4 - Prob. 153PECh. 4 - Prob. 154PECh. 4 - Prob. 1AAECh. 4 - Prob. 2AAECh. 4 - Prob. 3AAECh. 4 - Prob. 4AAECh. 4 - Prob. 5AAECh. 4 - Prob. 6AAECh. 4 - Prob. 7AAECh. 4 - Prob. 8AAECh. 4 - Prob. 9AAECh. 4 - Prob. 10AAECh. 4 - Prob. 11AAECh. 4 - Prob. 12AAECh. 4 - Prob. 13AAECh. 4 - Prob. 14AAECh. 4 - Prob. 15AAECh. 4 - Prob. 16AAECh. 4 - Prob. 17AAECh. 4 - Prob. 18AAECh. 4 - Prob. 19AAECh. 4 - Prob. 20AAECh. 4 - Prob. 21AAECh. 4 - Prob. 22AAECh. 4 - Prob. 23AAECh. 4 - Prob. 24AAECh. 4 - Prob. 25AAECh. 4 - Prob. 26AAECh. 4 - Prob. 27AAECh. 4 - Prob. 28AAECh. 4 - Prob. 29AAECh. 4 - Prob. 30AAECh. 4 - Prob. 31AAECh. 4 - Prob. 32AAECh. 4 - Prob. 33AAECh. 4 - Prob. 34AAECh. 4 - Prob. 35AAECh. 4 - Prob. 36AAECh. 4 - Prob. 37AAECh. 4 - Prob. 38AAECh. 4 - Prob. 39AAE
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Differential Equation | MIT 18.01SC Single Variable Calculus, Fall 2010; Author: MIT OpenCourseWare;https://www.youtube.com/watch?v=HaOHUfymsuk;License: Standard YouTube License, CC-BY