Thomas' Calculus: Early Transcendentals (14th Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
14th Edition
ISBN: 9780134439020
Author: Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher: PEARSON
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Chapter 4.2, Problem 62E
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Prove that there is at least one point between a and b such that the line tangent to the graphs of function f and g are parallel. Sketch the functions.

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Chapter 4 Solutions

Thomas' Calculus: Early Transcendentals (14th Edition)

Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - Prob. 2ECh. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 4.1 - In Exercises 1–6, determine from the graph whether...Ch. 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 - In Exercises 7–10, find the absolute extreme...Ch. 4.1 - Prob. 10E
Ch. 4.1 - In Exercises 11–14, match the table with a...Ch. 4.1 - In Exercises 11–14, match the table with a...Ch. 4.1 - In Exercises 11–14, match the table with a...Ch. 4.1 - In Exercises 11–14, match the table with a...Ch. 4.1 - In Exercises 15–20, sketch the graph of each...Ch. 4.1 - Prob. 16ECh. 4.1 - In Exercises 15-20, sketch the graph of each...Ch. 4.1 - Prob. 18ECh. 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. 21ECh. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - In Exercises 21–36, find the absolute maximum and...Ch. 4.1 - Prob. 30ECh. 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. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - In Exercises 21–40, find the absolute maximum and...Ch. 4.1 - In Exercises 21–40, find the absolute maximum and...Ch. 4.1 - In Exercises 21–40, find the absolute maximum and...Ch. 4.1 - In Exercises 21–40, find the absolute maximum and...Ch. 4.1 - In Exercises 41–44, find the function’s absolute...Ch. 4.1 - In Exercises 41–44, find the function’s absolute...Ch. 4.1 - In Exercises 41–44, find the function’s absolute...Ch. 4.1 - Prob. 44ECh. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - Prob. 46ECh. 4.1 - In Exercises 45–56, determine all critical points...Ch. 4.1 - Prob. 48ECh. 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. 52ECh. 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. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - Prob. 60ECh. 4.1 - Prob. 61ECh. 4.1 - In Exercises 57–64, find the critical points and...Ch. 4.1 - Prob. 63ECh. 4.1 - Prob. 64ECh. 4.1 - Prob. 65ECh. 4.1 - Prob. 66ECh. 4.1 - Prob. 67ECh. 4.1 - Prob. 68ECh. 4.1 - In Exercises 67–70, show that the function has...Ch. 4.1 - Prob. 70ECh. 4.1 - Prob. 71ECh. 4.1 - Prob. 72ECh. 4.1 - Prob. 73ECh. 4.1 - Prob. 74ECh. 4.1 - Prob. 75ECh. 4.1 - Prob. 76ECh. 4.1 - Prob. 77ECh. 4.1 - Prob. 78ECh. 4.1 - Prob. 79ECh. 4.1 - Prob. 80ECh. 4.1 - Prob. 81ECh. 4.1 - Prob. 82ECh. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Checking the Mean Value Theorem Find the value or...Ch. 4.2 - Find the value or values of c that satisfy the...Ch. 4.2 - Which of the functions in Exercises 9-14 satisfy...Ch. 4.2 - Prob. 10ECh. 4.2 - Prob. 11ECh. 4.2 - Prob. 12ECh. 4.2 - Which of the functions in Exercises 9–14 satisfy...Ch. 4.2 - Which of the functions in Exercises 9–14 satisfy...Ch. 4.2 - The function is zero at x = 0 and x = 1 and...Ch. 4.2 - For what values of a, m, and b does the...Ch. 4.2 - Plot the zeros of each polynomial on a line...Ch. 4.2 - Suppose that f″ is continuous on [a, b] and that f...Ch. 4.2 - Show that if f″ > 0 throughout an interval [a, b],...Ch. 4.2 - Show that a cubic polynomial can have at most...Ch. 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 - Show that the functions in Exercises 21–28 have...Ch. 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 - Show that the functions in Exercises 21–28 have...Ch. 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 - Suppose that f(–1) = 3 and that f′(x) = 0 for all...Ch. 4.2 - Suppose that f(0) = 5 and that f'(x) = 2 for all...Ch. 4.2 - Suppose that f'(x) = 2x for all x. Find f(2)...Ch. 4.2 - Prob. 32ECh. 4.2 - In Exercises 33–38, find all possible functions...Ch. 4.2 - In Exercises 33–38, find all possible functions...Ch. 4.2 - Prob. 35ECh. 4.2 - Prob. 36ECh. 4.2 - Prob. 37ECh. 4.2 - In Exercises 33–38, find all possible functions...Ch. 4.2 - In Exercises 39–42, find the function with the...Ch. 4.2 - In Exercises 39–42, find the function with the...Ch. 4.2 - In Exercises 39–42, find the function with the...Ch. 4.2 - In Exercises 39–42, find the function with the...Ch. 4.2 - Exercises 43–46 give the velocity v = ds/dt and...Ch. 4.2 - Prob. 44ECh. 4.2 - Exercises 43–46 give the velocity v = ds/dt and...Ch. 4.2 - Exercises 43–46 give the velocity v = ds/dt and...Ch. 4.2 - Prob. 47ECh. 4.2 - Prob. 48ECh. 4.2 - Prob. 49ECh. 4.2 - Exercises 47–50 give the acceleration , initial...Ch. 4.2 - Temperature change It took 14 sec for a mercury...Ch. 4.2 - A trucker handed in a ticket at a toll booth...Ch. 4.2 - Prob. 53ECh. 4.2 - A marathoner ran the 26.2-mi New York City...Ch. 4.2 - Prob. 55ECh. 4.2 - Free fall on the moon On our moon, the...Ch. 4.2 - The geometric mean of a and b The geometric mean...Ch. 4.2 - The arithmetic mean of a and b The arithmetic mean...Ch. 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 - Show that for any numbers a and b, the sine...Ch. 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 - Let f be differentiable at every value of x and...Ch. 4.2 - Let f(x) = px2 + qx + r be a quadratic function...Ch. 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 - Answer the following questions about the functions...Ch. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 4ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 8ECh. 4.3 - Prob. 9ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - Prob. 11ECh. 4.3 - Prob. 12ECh. 4.3 - Prob. 13ECh. 4.3 - Answer the following questions about the functions...Ch. 4.3 - In Exercises 15–18: Find the open intervals on...Ch. 4.3 - In Exercises 15–18: Find the open intervals on...Ch. 4.3 - Prob. 17ECh. 4.3 - In Exercises 15–18: 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 - 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. 23ECh. 4.3 - Prob. 24ECh. 4.3 - Prob. 25ECh. 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 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - Prob. 32ECh. 4.3 - Prob. 33ECh. 4.3 - Prob. 34ECh. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - Prob. 36ECh. 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. 39ECh. 4.3 - Find the open intervals on which the function is...Ch. 4.3 - Prob. 41ECh. 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. 44ECh. 4.3 - Prob. 45ECh. 4.3 - In Exercises 19–46: Find the open intervals on...Ch. 4.3 - In Exercises 47–58: Identify the function’s local...Ch. 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 - Prob. 55ECh. 4.3 - Prob. 56ECh. 4.3 - Prob. 57ECh. 4.3 - In Exercises 47–58: Identify the function’s local...Ch. 4.3 - Prob. 59ECh. 4.3 - Prob. 60ECh. 4.3 - In Exercises 59–66: Find the local extrema of each...Ch. 4.3 - Prob. 62ECh. 4.3 - In Exercises 59–66: Find the local extrema of each...Ch. 4.3 - Prob. 64ECh. 4.3 - Prob. 65ECh. 4.3 - In Exercises 59–66: Find the local extrema of each...Ch. 4.3 - Prob. 67ECh. 4.3 - Prob. 68ECh. 4.3 - Prob. 69ECh. 4.3 - Prob. 70ECh. 4.3 - Prob. 71ECh. 4.3 - Prob. 72ECh. 4.3 - Prob. 73ECh. 4.3 - Prob. 74ECh. 4.3 - Prob. 75ECh. 4.3 - Prob. 76ECh. 4.3 - Determine the values of constants a and b so that...Ch. 4.3 - Determine the values of constants a, b, c, and d...Ch. 4.3 - Locate and identify the absolute extreme values...Ch. 4.3 - Prove that f(x) = x − ln x is increasing for x >...Ch. 4.3 - Find the absolute maximum and the absolute minimum...Ch. 4.3 - Where does the periodic function f(x) = 2esin...Ch. 4.3 - Find the absolute maximum value of f(x) = x2 ln...Ch. 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 - 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. 5ECh. 4.4 - Prob. 6ECh. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - Identify the inflection points and local maxima...Ch. 4.4 - In Exercises 9-58, identify the coordinates of any...Ch. 4.4 - In Exercises 9-58, identify the coordinates of any...Ch. 4.4 - Prob. 11ECh. 4.4 - In Exercises 9-58, identify the coordinates of any...Ch. 4.4 - In Exercises 9-58, identify the coordinates of any...Ch. 4.4 - In Exercises 9-58, identify the coordinates of any...Ch. 4.4 - Prob. 15ECh. 4.4 - Prob. 16ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 20ECh. 4.4 - Prob. 21ECh. 4.4 - Prob. 22ECh. 4.4 - Prob. 23ECh. 4.4 - Prob. 24ECh. 4.4 - In Exercises 9–58, identify the coordinates of...Ch. 4.4 - Prob. 26ECh. 4.4 - Prob. 27ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 30ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 32ECh. 4.4 - Prob. 33ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 36ECh. 4.4 - Prob. 37ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 39ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of...Ch. 4.4 - Prob. 42ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 44ECh. 4.4 - Prob. 45ECh. 4.4 - Prob. 46ECh. 4.4 - Prob. 47ECh. 4.4 - Prob. 48ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 50ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 52ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 56ECh. 4.4 - Prob. 57ECh. 4.4 - In Exercises 9–58, identify the coordinates of any...Ch. 4.4 - Prob. 59ECh. 4.4 - Prob. 60ECh. 4.4 - Prob. 61ECh. 4.4 - Prob. 62ECh. 4.4 - Prob. 63ECh. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 4.4 - Prob. 66ECh. 4.4 - Prob. 67ECh. 4.4 - Prob. 68ECh. 4.4 - Prob. 69ECh. 4.4 - Prob. 70ECh. 4.4 - Prob. 71ECh. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 4.4 - Prob. 73ECh. 4.4 - Each of Exercises 71–92 gives the first derivative...Ch. 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 - Each of Exercises 93–96 shows the graphs of the...Ch. 4.4 - Prob. 83ECh. 4.4 - Prob. 84ECh. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Prob. 87ECh. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Prob. 90ECh. 4.4 - Prob. 91ECh. 4.4 - Prob. 92ECh. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Prob. 95ECh. 4.4 - Prob. 96ECh. 4.4 - Prob. 97ECh. 4.4 - Prob. 98ECh. 4.4 - Prob. 99ECh. 4.4 - Prob. 100ECh. 4.4 - Prob. 101ECh. 4.4 - Graph the rational functions in Exercises 85–102...Ch. 4.4 - Prob. 103ECh. 4.4 - Prob. 104ECh. 4.4 - Sketch the graph of a twice-differentiable...Ch. 4.4 - Prob. 106ECh. 4.4 - Prob. 107ECh. 4.4 - Prob. 108ECh. 4.4 - In Exercises 109 and 110, the graph of f′ is...Ch. 4.4 - In Exercises 109 and 110, the graph of f′ is...Ch. 4.4 - In Exercises 111 and 112, the graph of f′ is...Ch. 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 - Can anything be said about the graph of a function...Ch. 4.4 - Prob. 121ECh. 4.4 - Prob. 122ECh. 4.4 - Prob. 123ECh. 4.4 - Prob. 124ECh. 4.4 - Prob. 125ECh. 4.4 - Prob. 126ECh. 4.4 - Prob. 127ECh. 4.4 - Prob. 128ECh. 4.4 - Prob. 133ECh. 4.4 - Prob. 134ECh. 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 - 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 - 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. 7ECh. 4.5 - Prob. 8ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 10ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 18ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 24ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 26ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 30ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 36ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 38ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use 1’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 42ECh. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Use l’Hôpital’s rule to find the limits in...Ch. 4.5 - Prob. 50ECh. 4.5 - Find the limits in Exercises 51–66. 51. Ch. 4.5 - Prob. 52ECh. 4.5 - Find the limits in Exercises 51–66. 53. Ch. 4.5 - Prob. 54ECh. 4.5 - Find the limits in Exercises 51–66. 55. Ch. 4.5 - Find the limits in Exercises 51–66. 56. Ch. 4.5 - Prob. 57ECh. 4.5 - Find the limits in Exercises 51–66. 58. Ch. 4.5 - Find the limits in Exercises 51–66. 59. Ch. 4.5 - Find the limits in Exercises 51–66. 60. Ch. 4.5 - Find the limits in Exercises 51–66. 61. Ch. 4.5 - Prob. 62ECh. 4.5 - Find the limits in Exercises 51–66. 63. Ch. 4.5 - Find the limits in Exercises 51–66. 64. Ch. 4.5 - Prob. 65ECh. 4.5 - Find the limits in Exercises 51–66. 66. Ch. 4.5 - L’Hôpital’s Rule does not help with the limits in...Ch. 4.5 - Prob. 68ECh. 4.5 - Prob. 69ECh. 4.5 - L’Hôpital’s Rule does not help with the limits in...Ch. 4.5 - L’Hôpital’s Rule does not help with the limits in...Ch. 4.5 - L’Hôpital’s Rule does not help with the limits in...Ch. 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 - Find . Ch. 4.5 - Prob. 83ECh. 4.5 - This exercise explores the difference between the...Ch. 4.5 - Show that Ch. 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 - Prob. 2ECh. 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 - Designing a tank Your iron works has contracted to...Ch. 4.6 - Catching rainwater A 1125 ft3 open-top rectangular...Ch. 4.6 - Designing a poster You are designing a rectangular...Ch. 4.6 - Find the volume of the largest right circular cone...Ch. 4.6 - Two sides of a triangle have lengths a and b, and...Ch. 4.6 - Designing a can What are the dimensions of the...Ch. 4.6 - Designing a can You are designing a 1000 cm3 right...Ch. 4.6 - Designing a box with a lid A piece of cardboard...Ch. 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 - A window is in the form of a rectangle surmounted...Ch. 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 - Constructing cylinders Compare the answer to the...Ch. 4.6 - Constructing cones A right triangle whose...Ch. 4.6 - Prob. 28ECh. 4.6 - Find a positive number for which the sum of it and...Ch. 4.6 - Find a positive number for which the sum of its...Ch. 4.6 - Prob. 31ECh. 4.6 - Answer Exercise 31 if one piece is bent into a...Ch. 4.6 - Determine the dimensions of the rectangle of...Ch. 4.6 - Determine the dimensions of the rectangle of...Ch. 4.6 - Prob. 35ECh. 4.6 - Prob. 36ECh. 4.6 - Prob. 37ECh. 4.6 - Prob. 38ECh. 4.6 - Consider the accompanying graphs of y = 2x + 3 and...Ch. 4.6 - Find the point on the graph of y = 20x3 + 60x −...Ch. 4.6 - Prob. 41ECh. 4.6 - A cone is formed from a circular piece of material...Ch. 4.6 - Prob. 43ECh. 4.6 - Quickest route Jane is 2 mi offshore in a boat and...Ch. 4.6 - Shortest beam The 8-ft wall shown here stands 27...Ch. 4.6 - Motion on a line The positions of two particles on...Ch. 4.6 - Prob. 47ECh. 4.6 - Prob. 48ECh. 4.6 - Strength of a beam The strength S of a rectangular...Ch. 4.6 - Stiffness of a beam The stiffness S of a...Ch. 4.6 - Prob. 51ECh. 4.6 - Prob. 52ECh. 4.6 - Distance between two ships At noon, ship A was 12...Ch. 4.6 - Fermat’s principle in optics Light from a source A...Ch. 4.6 - Tin pest When metallic tin is kept below 13.2°C,...Ch. 4.6 - Airplane landing path An airplane is flying at...Ch. 4.6 - It costs you c dollars each to manufacture and...Ch. 4.6 - You operate a tour service that offers the...Ch. 4.6 - Wilson lot size formula One of the formulas for...Ch. 4.6 - Prob. 60ECh. 4.6 - Show that if r(x) = 6x and c(x) = x3 − 6x2 + 15x...Ch. 4.6 - Production level Suppose that c(x) = x3 − 20x2 +...Ch. 4.6 - You are to construct an open rectangular box with...Ch. 4.6 - Prob. 64ECh. 4.6 - Prob. 65ECh. 4.6 - How we cough When we cough, the trachea (windpipe)...Ch. 4.6 - Prob. 67ECh. 4.6 - Prob. 68ECh. 4.6 - Prob. 69ECh. 4.6 - You have been asked to determine whether the...Ch. 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 - Use Newton’s method to find an approximate...Ch. 4.7 - Prob. 8ECh. 4.7 - Use Newton’s method to find an approximate...Ch. 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 - Intersection of curves At what value(s) of x does...Ch. 4.7 - Prob. 24ECh. 4.7 - The graphs of y = x2(x + 1) and y = 1/x (x > 0)...Ch. 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 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 2ECh. 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 - 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 - 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. 12ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - In Exercises 1 -24, find an antiderivative for...Ch. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 16ECh. 4.8 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - In Exercises 1 -24, find an antiderivative for...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 - In Exercises 1–24, find an antiderivative for each...Ch. 4.8 - Prob. 22ECh. 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 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 - In Exercises 25–70, find the most general...Ch. 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 - In Exercises 25–70, find the most general...Ch. 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 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25–70, find the most general...Ch. 4.8 - Prob. 40ECh. 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 - 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 - 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 - 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. 54ECh. 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. 58ECh. 4.8 - In Exercises 25-70, find the most general...Ch. 4.8 - Prob. 60ECh. 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 - In Exercises 25–70, find the most general...Ch. 4.8 - In Exercises 25-70, find the most general...Ch. 4.8 - Prob. 66ECh. 4.8 - In Exercises 25-70, find the most general...Ch. 4.8 - Prob. 68ECh. 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. 71ECh. 4.8 - Prob. 72ECh. 4.8 - Prob. 73ECh. 4.8 - Verify the formulas in Exercises 71–82 by...Ch. 4.8 - Prob. 75ECh. 4.8 - Prob. 76ECh. 4.8 - Prob. 77ECh. 4.8 - Prob. 78ECh. 4.8 - Verify the formulas in Exercises 71–82 by...Ch. 4.8 - Prob. 80ECh. 4.8 - Verify the formulas in Exercises 71–82 by...Ch. 4.8 - Prob. 82ECh. 4.8 - Prob. 83ECh. 4.8 - Prob. 84ECh. 4.8 - Right, or wrong? Say which for each formula and...Ch. 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 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Prob. 100ECh. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Prob. 103ECh. 4.8 - Solve the initial value problems in Exercises...Ch. 4.8 - Solve the initial value problems in Exercises...Ch. 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 - Solve the initial value problems in Exercises...Ch. 4.8 - Find the curve y = f(x) in the xy-plane that...Ch. 4.8 - Find a curve y = f(x) with the following...Ch. 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 - Liftoff from Earth A rocket lifts off the surface...Ch. 4.8 - Stopping a car in time You are driving along a...Ch. 4.8 - Prob. 126ECh. 4.8 - Motion along a coordinate line A particle moves on...Ch. 4.8 - The hammer and the feather When Apollo 15...Ch. 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 - What are the hypotheses and conclusion of the Mean...Ch. 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 - In Exercises 1–16, find the extreme values...Ch. 4 - Prob. 4PECh. 4 - Prob. 5PECh. 4 - Prob. 6PECh. 4 - In Exercises 1–16, find the extreme values...Ch. 4 - Prob. 8PECh. 4 - Prob. 9PECh. 4 - Prob. 10PECh. 4 - In Exercises 1–16, find the extreme values...Ch. 4 - Prob. 12PECh. 4 - In Exercises 1–16, find the extreme values...Ch. 4 - Prob. 14PECh. 4 - Prob. 15PECh. 4 - Prob. 16PECh. 4 - Does f(x) = x3 + 2x + tan x have any local maximum...Ch. 4 - Prob. 18PECh. 4 - Prob. 19PECh. 4 - Prob. 20PECh. 4 - Prob. 21PECh. 4 - Prob. 22PECh. 4 - In Exercises 23 and 24, find the absolute maximum...Ch. 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 - Graph the curves in Exercises 43–58. 51. Ch. 4 - Prob. 52PECh. 4 - Graph the curves in Exercises 43–58. 53. Ch. 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 - Sketch the graphs of the rational functions in...Ch. 4 - Prob. 70PECh. 4 - Prob. 71PECh. 4 - Prob. 72PECh. 4 - Sketch the graphs of the rational functions in...Ch. 4 - Prob. 74PECh. 4 - Sketch the graphs of the rational functions in...Ch. 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 - Prob. 87PECh. 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 - The sum of two nonnegative numbers is 36. Find the...Ch. 4 - Prob. 104PECh. 4 - Prob. 105PECh. 4 - A customer has asked you to design an open-top...Ch. 4 - Find the height and radius of the largest right...Ch. 4 - The figure here shows two right circular cones,...Ch. 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 - Find the indefinite integrals (most general...Ch. 4 - Prob. 118PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 120PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 122PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 124PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 126PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 128PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 130PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 132PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 134PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 136PECh. 4 - Find the indefinite integrals (most general...Ch. 4 - Prob. 138PECh. 4 - Solve the initial value problems in Exercises...Ch. 4 - Prob. 140PECh. 4 - Solve the initial value problems in Exercise...Ch. 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 - Bounding a function Suppose that f is continuous...Ch. 4 - Prob. 8AAECh. 4 - Prob. 9AAECh. 4 - Prob. 10AAECh. 4 - Prob. 11AAECh. 4 - Prob. 12AAECh. 4 - Largest inscribed triangle Points A and B lie at...Ch. 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 - Can there be a curve satisfying the following...Ch. 4 - Find the equation for the curve in the xy-plane...Ch. 4 - A particle moves along the x-axis. Its...Ch. 4 - A particle moves with acceleration . Assuming that...Ch. 4 - Given f(x) = ax2 + 2bx + c with a > 0. By...Ch. 4 - Prob. 36AAECh. 4 - Prob. 37AAECh. 4 - Prob. 38AAECh. 4 - Prob. 39AAE
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Derivatives of Trigonometric Functions - Product Rule Quotient & Chain Rule - Calculus Tutorial; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=_niP0JaOgHY;License: Standard YouTube License, CC-BY