Problem 1E: In Exercises 1–4, solve for t.
1.
e−0.3t = 27
e(ln 0.2)t = 0.4
Problem 2E: In Exercises 1–4, solve for t.
2.
e−0.01t = 1000
Problem 3E: In Exercises 1–4, solve for t.
3.
Problem 4E Problem 5E: e2t − 3et = 0
Problem 6E: e−2t + 6 = 5e−t
Problem 7E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
7. y =... Problem 8E Problem 9E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
9. y =... Problem 10E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
10.
Problem 11E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
11. y = xex... Problem 12E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
12. y = (1 +... Problem 13E Problem 14E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
14. y = (9x2... Problem 15E Problem 16E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
56. y = ln... Problem 17E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
17.
Problem 18E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
18.
Problem 19E Problem 20E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
58. y = ln... Problem 21E Problem 22E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
60.
Problem 23E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
61. y =... Problem 24E: In Exercises 55-62, find the derivative of y with respect to x, t, or θ, as appropriate.
62. y =... Problem 25E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
25.
Problem 26E: In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
26.
Problem 27E: In Exercises 63-66, find dy/dx.
63. ln y = ey sin x
Problem 28E Problem 29E: In Exercises 27–32, find .
29.
Problem 30E Problem 31E: In Exercises 27–32, find dy/dx.
31. 3 + sin y = y − x3
Problem 32E Problem 33E: Evaluate the integrals in Exercises 33–54.
33.
Problem 34E: Evaluate the integrals in Exercises 33–54.
34.
Problem 35E Problem 36E Problem 37E Problem 38E Problem 39E Problem 40E: Evaluate the integrals in Exercises 33–54.
40.
Problem 41E: Evaluate the integrals in Exercises 1–46.
15.
Problem 42E: Evaluate the integrals in Exercises 1–46.
16.
Problem 43E: Evaluate the integrals in Exercises 1–46.
17.
Problem 44E Problem 45E: Evaluate the integrals in Exercises 1–46.
19.
Problem 46E Problem 47E Problem 48E: Evaluate the integrals in Exercises 33–54.
48.
Problem 49E Problem 50E Problem 51E: Evaluate the integrals in Exercises 1–46.
23.
Problem 52E: Evaluate the integrals in Exercises 1–46.
24.
Problem 53E Problem 54E: Evaluate the integrals in Exercises 1–46.
26.
Problem 55E: Solve the initial value problems in Exercises 55–58.
55.
Problem 56E: Solve the initial value problems in Exercises 55–58.
56.
Problem 57E: Solve the initial value problems in Exercises 55–58.
57.
Problem 58E Problem 59E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
67. y =... Problem 60E Problem 61E Problem 62E: In Exercises 67–88, find the derivative of y with respect to the given independent variable.
70.
Problem 63E Problem 64E Problem 65E Problem 66E: In Exercises 59–86, find the derivative of y with respect to the given independent variable.
66.
Problem 67E Problem 68E: In Exercises 59–86, find the derivative of y with respect to the given independent variable.
68.
Problem 69E Problem 70E: In Exercises 59–86, find the derivative of y with respect to the given independent variable.
70. y =... Problem 71E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
73. y =... Problem 72E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
74. y =... Problem 73E Problem 74E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
76
Problem 75E Problem 76E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
78. y =... Problem 77E Problem 78E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
80.
Problem 79E Problem 80E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
82.
Problem 81E: In Exercises 67-88, find the derivative of y with respect to the given independent variable.
83. y =... Problem 82E Problem 83E Problem 84E Problem 85E Problem 86E Problem 87E: Evaluate the integrals in Exercises 87–96.
87.
Problem 88E: Evaluate the integrals in Exercises 87–96.
88.
Problem 89E Problem 90E Problem 91E: Evaluate the integrals in Exercises 87–96.
91.
Problem 92E: Evaluate the integrals in Exercises 87–96.
92.
Problem 93E Problem 94E Problem 95E Problem 96E: Evaluate the integrals in Exercises 87–96.
96.
Problem 97E: Evaluate the integrals in Exercises 97–110.
97.
Problem 98E Problem 99E Problem 100E Problem 101E Problem 102E Problem 103E Problem 104E: Evaluate the integrals in Exercises 97–110.
104.
Problem 105E Problem 106E Problem 107E Problem 108E Problem 109E Problem 110E: Evaluate the integrals in Exercises 97–110.
110.
Problem 111E: Evaluate the integrals in Exercises 111–114.
111.
Problem 112E Problem 113E Problem 114E Problem 115E: In Exercises 89-100, use logarithmic differentiation or the method in Example 7 to find the... Problem 116E Problem 117E Problem 118E Problem 119E Problem 120E Problem 121E Problem 122E Problem 123E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 124E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 125E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 126E: In Exercises 89−100, use logarithmic differentiation or the method in Example 7 to find the... Problem 127E: For Exercises 127 and 128 find a function ƒ satisfying each equation.
127.
Problem 128E Problem 129E: Find the absolute maximum and minimum values of ƒ(x) = ex − 2x on [0, 1].
Problem 130E: Where does the periodic function ƒ(x) = 2esin(x/2) take on its extreme values and what are these... Problem 131E Problem 132E Problem 133E Problem 134E Problem 135E Problem 136E Problem 137E Problem 138E Problem 139E Problem 140E Problem 141E Problem 142E Problem 143E:
Show that ∫ ln x dx = x ln x − x + C.
Find the average value of ln x over [1, e].
Problem 144E Problem 145E Problem 146E: The linearization of ex at x = 0
Derive the linear approximation ex ≈ 1 + x at x = 0.
Estimate to... Problem 147E Problem 148E Problem 149E Problem 150E Problem 151E Problem 152E Problem 153E Problem 154E Problem 155E Problem 156E format_list_bulleted