CALCULUS WITH APPLICATIONS
11th Edition
ISBN: 2818440028601
Author: Lial
Publisher: XX SUPPLY
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Chapter 7.4, Problem 2E
To determine
To evaluate: The value of definite integral
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3. Consider the initial value problem
9y" +12y' + 4y = 0, y(0) = a>0: y′(0) = −1.
Solve the problem and find the value of a such that the solution of the initial value problem is always
positive.
5. Euler's equation.
Determine the values of a for which all solutions of the equation
5
x²y" + axy' + y = 0
that have the form (A + B log x) x* or Ax¹¹ + Bä” tend to zero as a approaches 0.
4. Problem on variable change.
The purpose of this problem is to perform an appropriate change of variables in order to reduce
the problem to a second-order equation with constant coefficients.
ty" + (t² − 1)y'′ + t³y = 0, 0
Chapter 7 Solutions
CALCULUS WITH APPLICATIONS
Ch. 7.1 - YOUR TURN 1 Find an antiderivative .
Ch. 7.1 - YOUR TURN 2
Find .
Ch. 7.1 - Prob. 3YTCh. 7.1 - Prob. 4YTCh. 7.1 - Prob. 5YTCh. 7.1 - Prob. 6YTCh. 7.1 - Prob. 7YTCh. 7.1 - Prob. 1WECh. 7.1 - Prob. 2WECh. 7.1 - Prob. 1E
Ch. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - 4. Explain why the restriction is necessary in...Ch. 7.1 - Find the following.
5.
Ch. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Find the following.
10.
Ch. 7.1 - Find the following.
11.
Ch. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Find the following.
16.
Ch. 7.1 - Prob. 17ECh. 7.1 - Prob. 18ECh. 7.1 - Prob. 19ECh. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Find the following.
22.
Ch. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Find the following.
26.
Ch. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Find the following.
32.
Ch. 7.1 - Find the following.
33.
Ch. 7.1 - Find the following.
34.
Ch. 7.1 - Prob. 35ECh. 7.1 - Find the following.
36.
Ch. 7.1 - Prob. 37ECh. 7.1 - Prob. 38ECh. 7.1 - Prob. 39ECh. 7.1 - Find the following.
40.
Ch. 7.1 - Prob. 41ECh. 7.1 - Find the following.
42.
Ch. 7.1 - Prob. 43ECh. 7.1 - Prob. 44ECh. 7.1 - Prob. 45ECh. 7.1 - Prob. 46ECh. 7.1 - Prob. 47ECh. 7.1 - Prob. 48ECh. 7.1 - Prob. 49ECh. 7.1 - Prob. 50ECh. 7.1 - Prob. 51ECh. 7.1 - Prob. 52ECh. 7.1 - Demand Find the demand function for each marginal...Ch. 7.1 - Prob. 54ECh. 7.1 - Demand Find the demand function for each marginal...Ch. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - 58. Profit The marginal profit of a small...Ch. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Prob. 61ECh. 7.1 - Prob. 62ECh. 7.1 - Prob. 63ECh. 7.1 - Prob. 64ECh. 7.1 - Prob. 65ECh. 7.1 - Prob. 66ECh. 7.1 - Prob. 67ECh. 7.1 - Prob. 68ECh. 7.1 - Prob. 69ECh. 7.1 - Exercises 67–71 refer to Example 11 in this...Ch. 7.1 - Prob. 71ECh. 7.1 - Prob. 72ECh. 7.1 - Prob. 73ECh. 7.1 - 74. Rocket Science In the 1999 movie October Sky,...Ch. 7.2 - YOUR TURN 1
Find
Ch. 7.2 - Prob. 2YTCh. 7.2 - Prob. 3YTCh. 7.2 - YOUR TURN 4
Find .
Ch. 7.2 - Prob. 5YTCh. 7.2 - Prob. 6YTCh. 7.2 - Prob. 1WECh. 7.2 - Prob. 2WECh. 7.2 - Prob. 3WECh. 7.2 - Prob. 1ECh. 7.2 - Prob. 2ECh. 7.2 - Prob. 3ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 5ECh. 7.2 - Prob. 6ECh. 7.2 - Prob. 7ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 10ECh. 7.2 - Prob. 11ECh. 7.2 - Prob. 12ECh. 7.2 - Prob. 13ECh. 7.2 - Prob. 14ECh. 7.2 - Prob. 15ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 17ECh. 7.2 - Prob. 18ECh. 7.2 - Prob. 19ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Use substitution to find each indefinite...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - 42. Profit The rate of growth of the profit (in...Ch. 7.2 - Prob. 43ECh. 7.2 - Prob. 44ECh. 7.2 - Prob. 45ECh. 7.2 - 46. Epidemic An epidemic is growing in a region...Ch. 7.3 - YOUR TURN 1 Repeat Example 1 to approximate
Ch. 7.3 - Prob. 2YTCh. 7.3 - Prob. 1ECh. 7.3 - Prob. 2ECh. 7.3 - Prob. 3ECh. 7.3 - 4. Let f(x) = 1/x, x1 = 1/2, x2 = 1, x3 = 3/2, x4...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - In Exercises 5–12, approximate the area under the...Ch. 7.3 - Prob. 13ECh. 7.3 - Prob. 14ECh. 7.3 - Prob. 15ECh. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Find the exact value of each integral using...Ch. 7.3 - Find the exact value of each integral using...Ch. 7.3 - Prob. 20ECh. 7.3 - Prob. 21ECh. 7.3 - Prob. 22ECh. 7.3 - In Exercises 24–30, estimate the area under each...Ch. 7.3 - Prob. 25ECh. 7.3 - Prob. 26ECh. 7.3 - Prob. 27ECh. 7.3 - Prob. 28ECh. 7.3 - Prob. 29ECh. 7.3 - Prob. 30ECh. 7.3 - Prob. 31ECh. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Prob. 37ECh. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.4 - YOUR TURN 1 Find .
Ch. 7.4 - Prob. 2YTCh. 7.4 - Prob. 3YTCh. 7.4 - Prob. 4YTCh. 7.4 - Prob. 5YTCh. 7.4 - Prob. 1WECh. 7.4 - Prob. 2WECh. 7.4 - Prob. 3WECh. 7.4 - Prob. 1ECh. 7.4 - Prob. 2ECh. 7.4 - Evaluate each definite integral.
3.
Ch. 7.4 - Evaluate each definite integral.
4.
Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Evaluate each definite integral.
7.
Ch. 7.4 - Evaluate each definite integral.
8.
Ch. 7.4 - Evaluate each definite integral.
9.
Ch. 7.4 - Evaluate each definite integral.
10.
Ch. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Evaluate each definite integral.
15.
Ch. 7.4 - Evaluate each definite integral.
16.
Ch. 7.4 - Evaluate each definite integral.
17.
Ch. 7.4 - Evaluate each definite integral.
18.
Ch. 7.4 - Evaluate each definite integral.
19.
Ch. 7.4 - Prob. 20ECh. 7.4 - Evaluate each definite integral.
21.
Ch. 7.4 - Evaluate each definite integral.
22.
Ch. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Evaluate each definite integral.
26.
Ch. 7.4 - Prob. 27ECh. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Evaluate each definite integral.
30.
Ch. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - In Exercises 31–40, use the definite integral to...Ch. 7.4 - Prob. 35ECh. 7.4 - Prob. 36ECh. 7.4 - Prob. 37ECh. 7.4 - In Exercises 31–40, use the definite integral to...Ch. 7.4 - Prob. 39ECh. 7.4 - Prob. 40ECh. 7.4 - Prob. 41ECh. 7.4 - Prob. 42ECh. 7.4 - Prob. 43ECh. 7.4 - Prob. 44ECh. 7.4 - Prob. 45ECh. 7.4 - Prob. 46ECh. 7.4 - Prob. 47ECh. 7.4 - Use the Fundamental Theorem to show that the...Ch. 7.4 - Prob. 49ECh. 7.4 - Prob. 50ECh. 7.4 - Prob. 51ECh. 7.4 - Prob. 52ECh. 7.4 - Prob. 53ECh. 7.4 - Prob. 54ECh. 7.4 - Business and Economies
55. Profit Karla Harby...Ch. 7.4 - 56. Worker Efficiency A worker new to a job will...Ch. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Prob. 61ECh. 7.4 - Prob. 62ECh. 7.4 - Prob. 63ECh. 7.4 - Prob. 64ECh. 7.4 - Prob. 65ECh. 7.4 - Prob. 66ECh. 7.4 - Prob. 67ECh. 7.4 - Prob. 68ECh. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.5 - YOUR TURN 1 Repeat Example 1 for f(x) = 4 – x2,...Ch. 7.5 - Prob. 2YTCh. 7.5 - Prob. 3YTCh. 7.5 - Prob. 4YTCh. 7.5 - Prob. 1WECh. 7.5 - Prob. 2WECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 15ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 17ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 19ECh. 7.5 - Prob. 20ECh. 7.5 - Prob. 21ECh. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Find the area between the curves in Exercises...Ch. 7.5 - Prob. 25ECh. 7.5 - Prob. 26ECh. 7.5 - Prob. 27ECh. 7.5 - Prob. 28ECh. 7.5 - Prob. 29ECh. 7.5 - Prob. 30ECh. 7.5 - Prob. 31ECh. 7.5 - 32. Producers’Surplus Suppose the supply function...Ch. 7.5 - Prob. 33ECh. 7.5 - 34. Consumers’ Surplus Find the consumers’ surplus...Ch. 7.5 - 35. Consumers’ and Producers’ Surplus Suppose the...Ch. 7.5 - 36. Consumers’ and Producers’ Surplus Suppose the...Ch. 7.5 - Prob. 37ECh. 7.5 - Prob. 38ECh. 7.5 - Prob. 39ECh. 7.5 - Prob. 40ECh. 7.5 - Prob. 41ECh. 7.5 - Prob. 42ECh. 7.6 - YOUR TURN 1 Use the trapezoidal rule with n = 4 to...Ch. 7.6 - Prob. 2YTCh. 7.6 - Prob. 1ECh. 7.6 - Prob. 2ECh. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - In Exercises 1–10, use n = 4 to approximate the...Ch. 7.6 - Prob. 11ECh. 7.6 - Prob. 12ECh. 7.6 - Prob. 13ECh. 7.6 - Prob. 14ECh. 7.6 - Prob. 15ECh. 7.6 - Prob. 16ECh. 7.6 - Prob. 17ECh. 7.6 - Prob. 18ECh. 7.6 - Prob. 19ECh. 7.6 - Prob. 20ECh. 7.6 - Prob. 21ECh. 7.6 - Prob. 22ECh. 7.6 - Prob. 23ECh. 7.6 - Prob. 24ECh. 7.6 - Prob. 25ECh. 7.6 - Prob. 26ECh. 7.6 - Prob. 27ECh. 7.6 - Prob. 28ECh. 7.6 - Prob. 29ECh. 7.6 - Prob. 30ECh. 7.6 - Prob. 31ECh. 7.6 - Prob. 32ECh. 7.6 - Prob. 33ECh. 7.6 - Prob. 34ECh. 7.6 - Prob. 35ECh. 7 - Prob. 1RECh. 7 - Prob. 2RECh. 7 - Prob. 3RECh. 7 - Prob. 4RECh. 7 - Prob. 5RECh. 7 - Prob. 6RECh. 7 - Prob. 7RECh. 7 - Prob. 8RECh. 7 - Prob. 9RECh. 7 - Prob. 10RECh. 7 - Prob. 11RECh. 7 - Prob. 12RECh. 7 - Prob. 13RECh. 7 - Prob. 14RECh. 7 - Prob. 15RECh. 7 - Prob. 16RECh. 7 - Prob. 17RECh. 7 - Prob. 18RECh. 7 - Prob. 19RECh. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Prob. 26RECh. 7 - Prob. 27RECh. 7 - Prob. 28RECh. 7 - Prob. 29RECh. 7 - Prob. 30RECh. 7 - Prob. 31RECh. 7 - Prob. 32RECh. 7 - Prob. 33RECh. 7 - Prob. 34RECh. 7 - Prob. 35RECh. 7 - Prob. 36RECh. 7 - Prob. 37RECh. 7 - Prob. 38RECh. 7 - Prob. 39RECh. 7 - Prob. 40RECh. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RECh. 7 - Prob. 44RECh. 7 - Prob. 45RECh. 7 - Prob. 46RECh. 7 - Prob. 47RECh. 7 - Prob. 48RECh. 7 - Prob. 49RECh. 7 - Prob. 50RECh. 7 - Prob. 51RECh. 7 - Prob. 52RECh. 7 - Prob. 53RECh. 7 - Prob. 54RECh. 7 - Prob. 55RECh. 7 - Prob. 56RECh. 7 - Prob. 57RECh. 7 - Prob. 58RECh. 7 - Prob. 59RECh. 7 - Prob. 60RECh. 7 - Prob. 61RECh. 7 - Prob. 62RECh. 7 - Prob. 63RECh. 7 - Prob. 64RECh. 7 - Prob. 65RECh. 7 - Prob. 66RECh. 7 - Prob. 67RECh. 7 - Prob. 68RECh. 7 - Prob. 69RECh. 7 - Prob. 70RECh. 7 - Prob. 71RECh. 7 - Prob. 72RECh. 7 - Prob. 73RECh. 7 - Prob. 74RECh. 7 - Prob. 75RECh. 7 - Prob. 76RECh. 7 - Prob. 77RECh. 7 - Prob. 78RECh. 7 - Prob. 79RECh. 7 - Prob. 80RECh. 7 - Prob. 81RECh. 7 - Prob. 82RECh. 7 - Prob. 83RECh. 7 - Prob. 84RECh. 7 - Prob. 85RECh. 7 - Prob. 86RECh. 7 - Prob. 87RECh. 7 - Prob. 88RECh. 7 - Prob. 89RECh. 7 - Prob. 90RECh. 7 - Prob. 91RECh. 7 - Prob. 92RECh. 7 - Prob. 93RECh. 7 - Prob. 94RECh. 7 - Prob. 95RE
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