University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
3rd Edition
ISBN: 9780321999610
Author: Joel R. Hass, Maurice D. Weir, George B. Thomas Jr.
Publisher: PEARSON
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Chapter 5.4, Problem 82E
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Chapter 5 Solutions
University Calculus: Early Transcendentals, Books a la Carte Edition (3rd Edition)
Ch. 5.1 - In Exercises 1–4, use finite approximations to...Ch. 5.1 - In Exercises 1–4, use finite approximations to...Ch. 5.1 - In Exercises 1–4, use finite approximations to...Ch. 5.1 - In Exercises 1–4, use finite approximations to...Ch. 5.1 - Prob. 5ECh. 5.1 - Using rectangles each of whose height is given by...Ch. 5.1 - Prob. 7ECh. 5.1 - Using rectangles each of whose height is given by...Ch. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
Ch. 5.1 - Length of a road You and a companion are about to...Ch. 5.1 - Prob. 12ECh. 5.1 - Free fall with air resistance An object is dropped...Ch. 5.1 - Prob. 14ECh. 5.1 - Prob. 15ECh. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - Prob. 18ECh. 5.1 - Water pollution Oil is leaking out of a tanker...Ch. 5.1 - Air pollution A power plant generates electricity...Ch. 5.1 - Inscribe a regular n-sided polygon inside a circle...Ch. 5.1 - Prob. 22ECh. 5.2 - Write the sums in Exercises 1–6 without sigma...Ch. 5.2 - Prob. 2ECh. 5.2 - Write the sums in Exercises 1–6 without sigma...Ch. 5.2 - Prob. 4ECh. 5.2 - Prob. 5ECh. 5.2 - Prob. 6ECh. 5.2 - Prob. 7ECh. 5.2 - Prob. 8ECh. 5.2 - Which formula is not equivalent to the other...Ch. 5.2 - Prob. 10ECh. 5.2 - Express the sums in Exercises 11–16 in sigma...Ch. 5.2 - Express the sums in Exercises 11–16 in sigma...Ch. 5.2 - Express the sums in Exercises 11–16 in sigma...Ch. 5.2 - Express the sums in Exercises 11–16 in sigma...Ch. 5.2 - Express the sums in Exercises 11–16 in sigma...Ch. 5.2 - Prob. 16ECh. 5.2 - Suppose that and . Find the values of
Ch. 5.2 - Suppose that and . Find the values of
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Evaluate the sums in Exercises 19–36.
Ch. 5.2 - Prob. 27ECh. 5.2 - Prob. 28ECh. 5.2 - Evaluate the sums in Exercises 19–36.
29.
Ch. 5.2 - Prob. 30ECh. 5.2 - Prob. 31ECh. 5.2 - Prob. 32ECh. 5.2 - In Exercises 37–42, graph each function f(x) over...Ch. 5.2 - Prob. 34ECh. 5.2 - Prob. 35ECh. 5.2 - In Exercises 37–42, graph each function f(x) over...Ch. 5.2 - Find the norm of the partition P = {0, 1.2, 1.5,...Ch. 5.2 - Find the norm of the partition P = {−2, −1.6,...Ch. 5.2 - Prob. 39ECh. 5.2 - Prob. 40ECh. 5.2 - Prob. 41ECh. 5.2 - Prob. 42ECh. 5.2 - Prob. 43ECh. 5.2 - Prob. 44ECh. 5.2 - Prob. 45ECh. 5.2 - Prob. 46ECh. 5.3 - Express the limits in Exercises 18 as definite...Ch. 5.3 - Prob. 2ECh. 5.3 - Prob. 3ECh. 5.3 - Prob. 4ECh. 5.3 - Prob. 5ECh. 5.3 - Prob. 6ECh. 5.3 - Prob. 7ECh. 5.3 - Express the limits in Exercises 1–8 as definite...Ch. 5.3 - Suppose that fand gare integrable and that...Ch. 5.3 - Suppose that f and h are integrable and that
, ,...Ch. 5.3 - Suppose that . Find
Ch. 5.3 - Prob. 12ECh. 5.3 - Suppose that f is integrable and that and ....Ch. 5.3 - Suppose that h is integrable and that and ....Ch. 5.3 - In Exercises 15–22, graph the integrands and use...Ch. 5.3 - Prob. 16ECh. 5.3 - In Exercises 15–22, graph the integrands and use...Ch. 5.3 - Prob. 18ECh. 5.3 - In Exercises 15–22, graph the integrands and use...Ch. 5.3 - In Exercises 15–22, graph the integrands and use...Ch. 5.3 - Prob. 21ECh. 5.3 - In Exercises 15–22, graph the integrands and use...Ch. 5.3 - Prob. 23ECh. 5.3 - Prob. 24ECh. 5.3 - Prob. 25ECh. 5.3 - Prob. 26ECh. 5.3 - Use known area formulas to evaluate the integrals...Ch. 5.3 - Prob. 28ECh. 5.3 - Prob. 29ECh. 5.3 - Prob. 30ECh. 5.3 - Prob. 31ECh. 5.3 - Prob. 32ECh. 5.3 - Prob. 33ECh. 5.3 - Prob. 34ECh. 5.3 - Prob. 35ECh. 5.3 - Prob. 36ECh. 5.3 - Prob. 37ECh. 5.3 - Prob. 38ECh. 5.3 - Prob. 39ECh. 5.3 - Prob. 40ECh. 5.3 - Prob. 41ECh. 5.3 - Prob. 42ECh. 5.3 - Prob. 43ECh. 5.3 - Prob. 44ECh. 5.3 - Prob. 45ECh. 5.3 - Prob. 46ECh. 5.3 - Prob. 47ECh. 5.3 - Use the rules in Table 5.6 and Equations(2)–(4) to...Ch. 5.3 - Prob. 49ECh. 5.3 - Prob. 50ECh. 5.3 - In Exercises 51–54, use a definite integral to...Ch. 5.3 - Prob. 52ECh. 5.3 - Prob. 53ECh. 5.3 - Prob. 54ECh. 5.3 - Prob. 55ECh. 5.3 - Prob. 56ECh. 5.3 - Prob. 57ECh. 5.3 - In Exercises 55–62, graph the function and find...Ch. 5.3 - Prob. 59ECh. 5.3 - Prob. 60ECh. 5.3 - Prob. 61ECh. 5.3 - In Exercises 55–62, graph the function and find...Ch. 5.3 - Prob. 63ECh. 5.3 - Prob. 64ECh. 5.3 - Use the method of Example 4a or Equation (1) to...Ch. 5.3 - Prob. 66ECh. 5.3 - Use the method of Example 4a or Equation (1) to...Ch. 5.3 - Prob. 68ECh. 5.3 - Prob. 69ECh. 5.3 - Prob. 70ECh. 5.3 - Prob. 71ECh. 5.3 - Prob. 72ECh. 5.3 - Prob. 73ECh. 5.3 - Prob. 74ECh. 5.3 - Prob. 75ECh. 5.3 - Prob. 76ECh. 5.3 - Prob. 77ECh. 5.3 - Prob. 78ECh. 5.3 - Prob. 79ECh. 5.3 - Prob. 80ECh. 5.3 - Prob. 81ECh. 5.3 - It would be nice if average values of integrable...Ch. 5.3 - Prob. 83ECh. 5.3 - Prob. 84ECh. 5.3 - Prob. 85ECh. 5.3 - Prob. 86ECh. 5.3 - Prob. 87ECh. 5.3 - Prob. 88ECh. 5.4 - Evaluate the integrals in Exercises 1–34.
1.
Ch. 5.4 - Prob. 2ECh. 5.4 - Prob. 3ECh. 5.4 - Prob. 4ECh. 5.4 - Evaluate the integrals in Exercises 1–34.
5.
Ch. 5.4 - Prob. 6ECh. 5.4 - Evaluate the integrals in Exercises 134. 7....Ch. 5.4 - Prob. 8ECh. 5.4 - Evaluate the integrals in Exercises 134. 9....Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
10.
Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
11.
Ch. 5.4 - Prob. 12ECh. 5.4 - Evaluate the integrals in Exercises 134. 13....Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
14.
Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
15.
Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
16.
Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
17.
Ch. 5.4 - Prob. 18ECh. 5.4 - Evaluate the integrals in Exercises 134. 19....Ch. 5.4 - Evaluate the integrals in Exercises 1–34.
20.
Ch. 5.4 - Evaluate the integrals in Exercises 134. 21....Ch. 5.4 - Prob. 22ECh. 5.4 - Evaluate the integrals in Exercises 1–34.
23.
Ch. 5.4 - Prob. 24ECh. 5.4 - Prob. 25ECh. 5.4 - Prob. 26ECh. 5.4 - Prob. 27ECh. 5.4 - Evaluate the integrals in Exercises 1–34.
28.
Ch. 5.4 - Evaluate the integrals in Exercises 134. 29....Ch. 5.4 - Prob. 30ECh. 5.4 - Evaluate the integrals in Exercises 1–34.
31.
Ch. 5.4 - Prob. 32ECh. 5.4 - Prob. 33ECh. 5.4 - Prob. 34ECh. 5.4 - Prob. 35ECh. 5.4 - Prob. 36ECh. 5.4 - Prob. 37ECh. 5.4 - In Exercises 35–38, guess an antiderivative for...Ch. 5.4 - Find the derivatives in Exercises 39–44.
by...Ch. 5.4 - Find the derivatives in Exercises 3944. by...Ch. 5.4 - Prob. 41ECh. 5.4 - Prob. 42ECh. 5.4 - Find the derivatives in Exercises 39–44.
by...Ch. 5.4 - Prob. 44ECh. 5.4 - Prob. 45ECh. 5.4 - Find dy/dx in Exercises 45–56.
46. , x > 0
Ch. 5.4 - Prob. 47ECh. 5.4 - Prob. 48ECh. 5.4 - Prob. 49ECh. 5.4 - Prob. 50ECh. 5.4 - Prob. 51ECh. 5.4 - Find dy/dx in Exercises 45–56.
52.
Ch. 5.4 - Prob. 53ECh. 5.4 - Prob. 54ECh. 5.4 - Prob. 55ECh. 5.4 - Prob. 56ECh. 5.4 - In Exercises 5760, find the total area between the...Ch. 5.4 - Prob. 58ECh. 5.4 - In Exercises 57–60, find the total area between...Ch. 5.4 - Prob. 60ECh. 5.4 - Prob. 61ECh. 5.4 - Prob. 62ECh. 5.4 - Prob. 63ECh. 5.4 - Prob. 64ECh. 5.4 - Prob. 65ECh. 5.4 - Prob. 66ECh. 5.4 - Prob. 67ECh. 5.4 - Prob. 68ECh. 5.4 - Prob. 69ECh. 5.4 - Prob. 70ECh. 5.4 - Prob. 71ECh. 5.4 - Prob. 72ECh. 5.4 - Prob. 73ECh. 5.4 - Prob. 74ECh. 5.4 - Prob. 75ECh. 5.4 - Prob. 76ECh. 5.4 - Prob. 77ECh. 5.4 - Prob. 78ECh. 5.4 - Prob. 79ECh. 5.4 - Prob. 80ECh. 5.4 - Prob. 81ECh. 5.4 - Prob. 82ECh. 5.4 - Prob. 83ECh. 5.4 - Prob. 84ECh. 5.5 - In Exercises 116, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - Prob. 4ECh. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - Prob. 12ECh. 5.5 - Prob. 13ECh. 5.5 - Prob. 14ECh. 5.5 - In Exercises 1–16, make the given substitutions to...Ch. 5.5 - Prob. 16ECh. 5.5 - Evaluate the integrals in Exercises 1766. 17....Ch. 5.5 - Evaluate the integrals in Exercises 17–66.
18.
Ch. 5.5 - Evaluate the integrals in Exercises 17–66.
19.
Ch. 5.5 - Prob. 20ECh. 5.5 - Evaluate the integrals in Exercises 1766. 21....Ch. 5.5 - Prob. 22ECh. 5.5 - Evaluate the integrals in Exercises 1766. 23....Ch. 5.5 - Prob. 24ECh. 5.5 - Evaluate the integrals in Exercises 1766. 25....Ch. 5.5 - Evaluate the integrals in Exercises 17–66.
26.
Ch. 5.5 - Evaluate the integrals in Exercises 17–66.
27.
Ch. 5.5 - Prob. 28ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
29.
Ch. 5.5 - Prob. 30ECh. 5.5 - Evaluate the integrals in Exercises 1766. 31....Ch. 5.5 - Prob. 32ECh. 5.5 - Prob. 33ECh. 5.5 - Prob. 34ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
35.
Ch. 5.5 - Prob. 36ECh. 5.5 - Prob. 37ECh. 5.5 - Prob. 38ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
39.
Ch. 5.5 - Prob. 40ECh. 5.5 - Evaluate the integrals in Exercises 1766. 41....Ch. 5.5 - Prob. 42ECh. 5.5 - Evaluate the integrals in Exercises 1766....Ch. 5.5 - Prob. 44ECh. 5.5 - Prob. 45ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
46.
Ch. 5.5 - Prob. 47ECh. 5.5 - Prob. 48ECh. 5.5 - Prob. 49ECh. 5.5 - Prob. 50ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
51.
Ch. 5.5 - Evaluate the integrals in Exercises 17–66.
52.
Ch. 5.5 - Prob. 53ECh. 5.5 - Prob. 54ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
55.
Ch. 5.5 - Prob. 56ECh. 5.5 - Evaluate the integrals in Exercises 17-66.
57.
Ch. 5.5 - Prob. 58ECh. 5.5 - Prob. 59ECh. 5.5 - Prob. 60ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
61.
Ch. 5.5 - Prob. 62ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
63.
Ch. 5.5 - Prob. 64ECh. 5.5 - Evaluate the integrals in Exercises 17–66.
65.
Ch. 5.5 - Prob. 66ECh. 5.5 - If you do not know what substitution to make, try...Ch. 5.5 - Prob. 68ECh. 5.5 - Prob. 69ECh. 5.5 - Prob. 70ECh. 5.5 - Prob. 71ECh. 5.5 - Prob. 72ECh. 5.5 - Solve the initial value problems in Exercises...Ch. 5.5 - Prob. 74ECh. 5.5 - Solve the initial value problems in Exercises...Ch. 5.5 - Prob. 76ECh. 5.5 - Prob. 77ECh. 5.5 - Prob. 78ECh. 5.5 - Prob. 79ECh. 5.5 - Prob. 80ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 3ECh. 5.6 - Prob. 4ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 6ECh. 5.6 - Prob. 7ECh. 5.6 - Prob. 8ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 10ECh. 5.6 - Prob. 11ECh. 5.6 - Prob. 12ECh. 5.6 - Prob. 13ECh. 5.6 - Prob. 14ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 16ECh. 5.6 - Prob. 17ECh. 5.6 - Prob. 18ECh. 5.6 - Prob. 19ECh. 5.6 - Prob. 20ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 22ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 24ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 26ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 28ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 30ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 34ECh. 5.6 - Prob. 35ECh. 5.6 - Prob. 36ECh. 5.6 - Prob. 37ECh. 5.6 - Prob. 38ECh. 5.6 - Use the Substitution Formula in Theorem 7 to...Ch. 5.6 - Prob. 40ECh. 5.6 - Prob. 41ECh. 5.6 - Prob. 42ECh. 5.6 - Prob. 43ECh. 5.6 - Prob. 44ECh. 5.6 - Prob. 45ECh. 5.6 - Prob. 46ECh. 5.6 - Prob. 47ECh. 5.6 - Prob. 48ECh. 5.6 - Prob. 49ECh. 5.6 - Prob. 50ECh. 5.6 - Find the total areas of the shaded regions in...Ch. 5.6 - Prob. 52ECh. 5.6 - Find the total areas of the shaded regions in...Ch. 5.6 - Prob. 54ECh. 5.6 - Find the total areas of the shaded regions in...Ch. 5.6 - Prob. 56ECh. 5.6 - Prob. 57ECh. 5.6 - Find the total areas of the shaded regions in...Ch. 5.6 - Find the total areas of the shaded regions in...Ch. 5.6 - Prob. 60ECh. 5.6 - Prob. 61ECh. 5.6 - Prob. 62ECh. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Prob. 71ECh. 5.6 - Prob. 72ECh. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Prob. 74ECh. 5.6 - Prob. 75ECh. 5.6 - Prob. 76ECh. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Prob. 78ECh. 5.6 - Prob. 79ECh. 5.6 - Prob. 80ECh. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Prob. 83ECh. 5.6 - Prob. 84ECh. 5.6 - Prob. 85ECh. 5.6 - Find the areas of the regions enclosed by the...Ch. 5.6 - Prob. 87ECh. 5.6 - Prob. 88ECh. 5.6 - Prob. 89ECh. 5.6 - Prob. 90ECh. 5.6 - Prob. 91ECh. 5.6 - Prob. 92ECh. 5.6 - Prob. 93ECh. 5.6 - Prob. 94ECh. 5.6 - Prob. 95ECh. 5.6 - Prob. 96ECh. 5.6 - Prob. 97ECh. 5.6 - Prob. 98ECh. 5.6 - Prob. 99ECh. 5.6 - Prob. 100ECh. 5.6 - Prob. 101ECh. 5.6 - Prob. 102ECh. 5.6 - Prob. 103ECh. 5.6 - Prob. 104ECh. 5.6 - Prob. 105ECh. 5.6 - Prob. 106ECh. 5.6 - Prob. 107ECh. 5.6 - Prob. 108ECh. 5.6 - Prob. 109ECh. 5.6 - Prob. 110ECh. 5.6 - Prob. 111ECh. 5.6 - Prob. 112ECh. 5.6 - Prob. 113ECh. 5.6 - Prob. 114ECh. 5.6 - Prob. 115ECh. 5.6 - Prob. 116ECh. 5.6 - Prob. 117ECh. 5.6 - Prob. 118ECh. 5 - How can you sometimes estimate quantities like...Ch. 5 - Prob. 2GYRCh. 5 - Prob. 3GYRCh. 5 - Prob. 4GYRCh. 5 - Prob. 5GYRCh. 5 - Prob. 6GYRCh. 5 - Prob. 7GYRCh. 5 - Prob. 8GYRCh. 5 - Prob. 9GYRCh. 5 - Prob. 10GYRCh. 5 - Prob. 11GYRCh. 5 - Prob. 12GYRCh. 5 - Prob. 13GYRCh. 5 - Prob. 14GYRCh. 5 - Prob. 15GYRCh. 5 - Prob. 16GYRCh. 5 - Prob. 1PECh. 5 - Prob. 2PECh. 5 - Prob. 3PECh. 5 - Prob. 4PECh. 5 - Prob. 5PECh. 5 - Prob. 6PECh. 5 - Prob. 7PECh. 5 - Prob. 8PECh. 5 - Prob. 9PECh. 5 - Prob. 10PECh. 5 - Prob. 11PECh. 5 - Prob. 12PECh. 5 - Prob. 13PECh. 5 - Prob. 14PECh. 5 - Prob. 15PECh. 5 - Prob. 16PECh. 5 - Prob. 17PECh. 5 - Prob. 18PECh. 5 - Prob. 19PECh. 5 - Prob. 20PECh. 5 - Prob. 21PECh. 5 - Prob. 22PECh. 5 - Prob. 23PECh. 5 - Prob. 24PECh. 5 - Prob. 25PECh. 5 - Prob. 26PECh. 5 - Prob. 27PECh. 5 - Prob. 28PECh. 5 - Prob. 29PECh. 5 - Prob. 30PECh. 5 - Prob. 31PECh. 5 - Find the total area of the region between the...Ch. 5 - Prob. 33PECh. 5 - Prob. 34PECh. 5 - Prob. 35PECh. 5 - Prob. 36PECh. 5 - Prob. 37PECh. 5 - Prob. 38PECh. 5 - Prob. 39PECh. 5 - Prob. 40PECh. 5 - Prob. 41PECh. 5 - Prob. 42PECh. 5 - Prob. 43PECh. 5 - Prob. 44PECh. 5 - Prob. 45PECh. 5 - Prob. 46PECh. 5 - Prob. 47PECh. 5 - Prob. 48PECh. 5 - Prob. 49PECh. 5 - Prob. 50PECh. 5 - Prob. 51PECh. 5 - Prob. 52PECh. 5 - Prob. 53PECh. 5 - Prob. 54PECh. 5 - Prob. 55PECh. 5 - Prob. 56PECh. 5 - Prob. 57PECh. 5 - Prob. 58PECh. 5 - Prob. 59PECh. 5 - Prob. 60PECh. 5 - Prob. 61PECh. 5 - Prob. 62PECh. 5 - Prob. 63PECh. 5 - Prob. 64PECh. 5 - Prob. 65PECh. 5 - Prob. 66PECh. 5 - Prob. 67PECh. 5 - Prob. 68PECh. 5 - Prob. 69PECh. 5 - Prob. 70PECh. 5 - Prob. 71PECh. 5 - Prob. 72PECh. 5 - Prob. 73PECh. 5 - Prob. 74PECh. 5 - Prob. 75PECh. 5 - Prob. 76PECh. 5 - Prob. 77PECh. 5 - Prob. 78PECh. 5 - Prob. 79PECh. 5 - Prob. 80PECh. 5 - Prob. 81PECh. 5 - Prob. 82PECh. 5 - Prob. 83PECh. 5 - Prob. 84PECh. 5 - Prob. 85PECh. 5 - Prob. 86PECh. 5 - Prob. 87PECh. 5 - Prob. 88PECh. 5 - Prob. 89PECh. 5 - Evaluate the integrals in Exercises 77–116.
94.
Ch. 5 - Prob. 91PECh. 5 - Prob. 92PECh. 5 - Prob. 93PECh. 5 - Prob. 94PECh. 5 - Prob. 95PECh. 5 - Prob. 96PECh. 5 - Prob. 97PECh. 5 - Prob. 98PECh. 5 - Prob. 99PECh. 5 - Prob. 100PECh. 5 - Prob. 101PECh. 5 - Prob. 102PECh. 5 - Prob. 103PECh. 5 - Prob. 104PECh. 5 - Prob. 105PECh. 5 - Prob. 106PECh. 5 - Prob. 107PECh. 5 - Prob. 108PECh. 5 - Prob. 109PECh. 5 - Prob. 110PECh. 5 - Prob. 111PECh. 5 - Prob. 112PECh. 5 - Prob. 113PECh. 5 - Prob. 114PECh. 5 - Prob. 115PECh. 5 - Prob. 116PECh. 5 - Prob. 117PECh. 5 - Prob. 118PECh. 5 - Prob. 119PECh. 5 - Prob. 120PECh. 5 - Prob. 121PECh. 5 - Prob. 122PECh. 5 - Prob. 123PECh. 5 - Prob. 124PECh. 5 - Prob. 125PECh. 5 - Prob. 126PECh. 5 - Prob. 127PECh. 5 - Prob. 128PECh. 5 - Prob. 1AAECh. 5 - Prob. 2AAECh. 5 - Prob. 3AAECh. 5 - Prob. 4AAECh. 5 - Prob. 5AAECh. 5 - Prob. 6AAECh. 5 - Prob. 7AAECh. 5 - Prob. 8AAECh. 5 - Prob. 9AAECh. 5 - Prob. 10AAECh. 5 - Prob. 11AAECh. 5 - Prob. 12AAECh. 5 - Prob. 13AAECh. 5 - Prob. 14AAECh. 5 - Prob. 15AAECh. 5 - Prob. 16AAECh. 5 - Prob. 17AAECh. 5 - Prob. 18AAECh. 5 - Prob. 19AAECh. 5 - Prob. 20AAECh. 5 - Prob. 21AAECh. 5 - Prob. 22AAECh. 5 - Prob. 23AAECh. 5 - Prob. 24AAECh. 5 - Prob. 25AAECh. 5 - Prob. 26AAECh. 5 - Prob. 27AAECh. 5 - Prob. 28AAECh. 5 - Prob. 29AAECh. 5 - Prob. 30AAECh. 5 - Prob. 31AAECh. 5 - Prob. 32AAECh. 5 - Prob. 33AAECh. 5 - Prob. 34AAECh. 5 - Prob. 35AAECh. 5 - Prob. 36AAECh. 5 - Prob. 37AAECh. 5 - Prob. 38AAECh. 5 - Prob. 39AAECh. 5 - Prob. 40AAE
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- For the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardFor the system consisting of the three planes:plane 1: -4x + 4y - 2z = -8plane 2: 2x + 2y + 4z = 20plane 3: -2x - 3y + z = -1a) Are any of the planes parallel and/or coincident? Justify your answer.b) Determine if the normals are coplanar. What does this tell you about the system?c) Solve the system if possible. Show a complete solution (do not use matrix operations). Classify the system using the terms: consistent, inconsistent, dependent and/or independent.arrow_forwardOpen your tool box and find geometric methods, symmetries of even and odd functions and the evaluation theorem. Use these to calculate the following definite integrals. Note that you should not use Riemann sums for this problem. (a) (4 pts) (b) (2 pts) 3 S³ 0 3-x+9-dz x3 + sin(x) x4 + cos(x) dx (c) (4 pts) L 1-|x|dxarrow_forward
- An engineer is designing a pipeline which is supposed to connect two points P and S. The engineer decides to do it in three sections. The first section runs from point P to point Q, and costs $48 per mile to lay, the second section runs from point Q to point R and costs $54 per mile, the third runs from point R to point S and costs $44 per mile. Looking at the diagram below, you see that if you know the lengths marked x and y, then you know the positions of Q and R. Find the values of x and y which minimize the cost of the pipeline. Please show your answers to 4 decimal places. 2 Miles x = 1 Mile R 10 miles miles y = milesarrow_forwardAn open-top rectangular box is being constructed to hold a volume of 150 in³. The base of the box is made from a material costing 7 cents/in². The front of the box must be decorated, and will cost 11 cents/in². The remainder of the sides will cost 3 cents/in². Find the dimensions that will minimize the cost of constructing this box. Please show your answers to at least 4 decimal places. Front width: Depth: in. in. Height: in.arrow_forwardFind and classify the critical points of z = (x² – 8x) (y² – 6y). Local maximums: Local minimums: Saddle points: - For each classification, enter a list of ordered pairs (x, y) where the max/min/saddle occurs. Enter DNE if there are no points for a classification.arrow_forward
- Suppose that f(x, y, z) = (x − 2)² + (y – 2)² + (z − 2)² with 0 < x, y, z and x+y+z≤ 10. 1. The critical point of f(x, y, z) is at (a, b, c). Then a = b = C = 2. Absolute minimum of f(x, y, z) is and the absolute maximum isarrow_forwardThe spread of an infectious disease is often modeled using the following autonomous differential equation: dI - - BI(N − I) − MI, dt where I is the number of infected people, N is the total size of the population being modeled, ẞ is a constant determining the rate of transmission, and μ is the rate at which people recover from infection. Close a) (5 points) Suppose ẞ = 0.01, N = 1000, and µ = 2. Find all equilibria. b) (5 points) For the equilbria in part a), determine whether each is stable or unstable. c) (3 points) Suppose ƒ(I) = d. Draw a phase plot of f against I. (You can use Wolfram Alpha or Desmos to plot the function, or draw the dt function by hand.) Identify the equilibria as stable or unstable in the graph. d) (2 points) Explain the biological meaning of these equilibria being stable or unstable.arrow_forwardFind the indefinite integral. Check Answer: 7x 4 + 1x dxarrow_forward
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