EBK CALCULUS: AN APPLIED APPROACH
10th Edition
ISBN: 8220101426222
Author: Larson
Publisher: CENGAGE L
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Chapter 6.3, Problem 7E
To determine
To calculate: The value of the integral
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Question 1. (10 points)
A researcher is studying tumours in mice. The growth rate for the volume of the tumour V(t) in cm³ is given by
dV
=
1.45V(2 In(V+1)).
dt
(a) (4 pts) Find all the equilibria and determine their stability using the stability condition.
(b) (2 pts) Draw the phase plot f(V) versus V where f(V) = V'. You may find it helpful to use Desmos or Wolfram Alpha to plot the graph of
f(V) versus V (both are free to use online), or you can plot it by hand if you like. On the plot identify each equilibrium as stable or unstable.
(c) (4 pts) Draw direction arrows for the case where the tumour starts at size 3cm³ and for the case where the tumour starts at size 9cm³. Explain
in biological terms what happens to the size of each of these tumours at time progresses.
For the system consisting of the two planes:plane 1: -x + y + z = 0plane 2: 3x + y + 3z = 0a) Are the planes parallel and/or coincident? Justify your answer. What does this tell you about the solution to the system?b) Solve the system (if possible). Show a complete solution. If there is a line of intersection express it in parametric form.
Question 2: (10 points) Evaluate the definite integral.
Use the following form of the definition of the integral to evaluate the integral:
Theorem: Iff is integrable on [a, b], then
where Ax = (ba)/n and x₂ = a + i^x.
You might need the following formulas.
IM³
L² (3x²
(3x²+2x-
2x - 1)dx.
n
[f(z)dz lim f(x)Az
a
n→∞
i=1
n(n + 1)
2
n
i=1
n(n+1)(2n+1)
6
Chapter 6 Solutions
EBK CALCULUS: AN APPLIED APPROACH
Ch. 6.1 - Prob. 1CPCh. 6.1 - Prob. 2CPCh. 6.1 - Prob. 3CPCh. 6.1 - Prob. 4CPCh. 6.1 - Prob. 5CPCh. 6.1 - Prob. 6CPCh. 6.1 - Prob. 7CPCh. 6.1 - Prob. 1SWUCh. 6.1 - Prob. 2SWUCh. 6.1 - Prob. 3SWU
Ch. 6.1 - Prob. 4SWUCh. 6.1 - Prob. 5SWUCh. 6.1 - Prob. 6SWUCh. 6.1 - Prob. 7SWUCh. 6.1 - Prob. 8SWUCh. 6.1 - Prob. 9SWUCh. 6.1 - Prob. 10SWUCh. 6.1 - Prob. 1ECh. 6.1 - Prob. 2ECh. 6.1 - Prob. 3ECh. 6.1 - Prob. 4ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 6ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 8ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 10ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 12ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 14ECh. 6.1 - Integration by Parts In Exercises 5-16, use...Ch. 6.1 - Prob. 16ECh. 6.1 - Prob. 17ECh. 6.1 - Prob. 18ECh. 6.1 - Prob. 19ECh. 6.1 - Prob. 20ECh. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 23ECh. 6.1 - Prob. 24ECh. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 26ECh. 6.1 - Prob. 27ECh. 6.1 - Prob. 28ECh. 6.1 - Prob. 29ECh. 6.1 - Prob. 30ECh. 6.1 - Prob. 31ECh. 6.1 - Prob. 32ECh. 6.1 - Prob. 33ECh. 6.1 - Prob. 34ECh. 6.1 - Prob. 35ECh. 6.1 - Prob. 36ECh. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Finding an Indefinite Integral In Exercises 17-38,...Ch. 6.1 - Prob. 39ECh. 6.1 - Prob. 40ECh. 6.1 - Prob. 41ECh. 6.1 - Evaluating a Definite Integral In Exercises 39-46,...Ch. 6.1 - Prob. 43ECh. 6.1 - Prob. 44ECh. 6.1 - Prob. 45ECh. 6.1 - Prob. 46ECh. 6.1 - Prob. 47ECh. 6.1 - Prob. 48ECh. 6.1 - Prob. 49ECh. 6.1 - Prob. 50ECh. 6.1 - Prob. 51ECh. 6.1 - Prob. 52ECh. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Verifying Formulas In Exercises 53 and 54, use...Ch. 6.1 - Prob. 55ECh. 6.1 - Prob. 56ECh. 6.1 - Prob. 57ECh. 6.1 - Prob. 58ECh. 6.1 - Prob. 59ECh. 6.1 - Prob. 60ECh. 6.1 - Prob. 61ECh. 6.1 - Prob. 62ECh. 6.1 - Prob. 63ECh. 6.1 - Prob. 64ECh. 6.1 - Prob. 65ECh. 6.1 - Revenue A company sells a seasonal product. The...Ch. 6.1 - Prob. 67ECh. 6.1 - Prob. 68ECh. 6.1 - Prob. 69ECh. 6.1 - Prob. 70ECh. 6.1 - Prob. 71ECh. 6.1 - Prob. 72ECh. 6.1 - Prob. 73ECh. 6.1 - Prob. 74ECh. 6.1 - Prob. 75ECh. 6.1 - Prob. 76ECh. 6.1 - Prob. 77ECh. 6.1 - Prob. 78ECh. 6.1 - Prob. 79ECh. 6.1 - Future Value In Exercises 79 and 80, find the...Ch. 6.1 - Prob. 81ECh. 6.1 - Prob. 82ECh. 6.2 - Checkpoint 1 Use the integration table in Appendix...Ch. 6.2 - Prob. 2CPCh. 6.2 - Prob. 3CPCh. 6.2 - Prob. 4CPCh. 6.2 - Checkpoint 5 Use the integration table in Appendix...Ch. 6.2 - Prob. 6CPCh. 6.2 - Prob. 1SWUCh. 6.2 - Prob. 2SWUCh. 6.2 - Prob. 3SWUCh. 6.2 - Prob. 4SWUCh. 6.2 - Prob. 5SWUCh. 6.2 - Prob. 6SWUCh. 6.2 - Prob. 1ECh. 6.2 - Prob. 2ECh. 6.2 - Using Integration Tables In Exercises 18, use the...Ch. 6.2 - Prob. 4ECh. 6.2 - Prob. 5ECh. 6.2 - Prob. 6ECh. 6.2 - Prob. 7ECh. 6.2 - Prob. 8ECh. 6.2 - Prob. 9ECh. 6.2 - Prob. 10ECh. 6.2 - Prob. 11ECh. 6.2 - Prob. 12ECh. 6.2 - Prob. 13ECh. 6.2 - Prob. 14ECh. 6.2 - Prob. 15ECh. 6.2 - Prob. 16ECh. 6.2 - Prob. 17ECh. 6.2 - Prob. 18ECh. 6.2 - Prob. 19ECh. 6.2 - Prob. 20ECh. 6.2 - Prob. 21ECh. 6.2 - Prob. 22ECh. 6.2 - Prob. 23ECh. 6.2 - Prob. 24ECh. 6.2 - Prob. 25ECh. 6.2 - Prob. 26ECh. 6.2 - Prob. 27ECh. 6.2 - Prob. 28ECh. 6.2 - Prob. 29ECh. 6.2 - Prob. 30ECh. 6.2 - Prob. 31ECh. 6.2 - Prob. 32ECh. 6.2 - Prob. 33ECh. 6.2 - Prob. 34ECh. 6.2 - Prob. 35ECh. 6.2 - Prob. 36ECh. 6.2 - Prob. 37ECh. 6.2 - Prob. 38ECh. 6.2 - Prob. 39ECh. 6.2 - Prob. 40ECh. 6.2 - Prob. 41ECh. 6.2 - Using Integration Tables In Exercises 37 44, use...Ch. 6.2 - Prob. 43ECh. 6.2 - Prob. 44ECh. 6.2 - Prob. 45ECh. 6.2 - Area of a Region In Exercises 45-50, use the...Ch. 6.2 - Prob. 47ECh. 6.2 - Prob. 48ECh. 6.2 - Prob. 49ECh. 6.2 - Prob. 50ECh. 6.2 - Prob. 51ECh. 6.2 - Prob. 52ECh. 6.2 - Prob. 53ECh. 6.2 - Prob. 54ECh. 6.2 - Prob. 55ECh. 6.2 - Probability The probability of finding between a...Ch. 6.2 - Population Growth In Exercises 57 and 58, use a...Ch. 6.2 - Prob. 58ECh. 6.2 - Prob. 59ECh. 6.2 - Prob. 60ECh. 6.2 - Prob. 61ECh. 6.2 - Prob. 1QYCh. 6.2 - Prob. 2QYCh. 6.2 - Prob. 3QYCh. 6.2 - In Exercises 16, use integration by parts to find...Ch. 6.2 - Prob. 5QYCh. 6.2 - Prob. 6QYCh. 6.2 - Prob. 7QYCh. 6.2 - Prob. 8QYCh. 6.2 - Prob. 9QYCh. 6.2 - Prob. 10QYCh. 6.2 - Prob. 11QYCh. 6.2 - Prob. 12QYCh. 6.2 - Prob. 13QYCh. 6.2 - Prob. 14QYCh. 6.2 - Prob. 15QYCh. 6.2 - Prob. 16QYCh. 6.2 - Prob. 17QYCh. 6.2 - Prob. 18QYCh. 6.2 - Prob. 19QYCh. 6.2 - Prob. 20QYCh. 6.2 - Prob. 21QYCh. 6.3 - Checkpoint 1 Use the Trapezoidal Rule with n = 4...Ch. 6.3 - Prob. 2CPCh. 6.3 - Prob. 3CPCh. 6.3 - Prob. 1SWUCh. 6.3 - Prob. 2SWUCh. 6.3 - Prob. 3SWUCh. 6.3 - Prob. 4SWUCh. 6.3 - Prob. 5SWUCh. 6.3 - Prob. 6SWUCh. 6.3 - Prob. 7SWUCh. 6.3 - Prob. 8SWUCh. 6.3 - Prob. 9SWUCh. 6.3 - Prob. 10SWUCh. 6.3 - Prob. 1ECh. 6.3 - Prob. 2ECh. 6.3 - Prob. 3ECh. 6.3 - Prob. 4ECh. 6.3 - Prob. 5ECh. 6.3 - Prob. 6ECh. 6.3 - Prob. 7ECh. 6.3 - Prob. 8ECh. 6.3 - Prob. 9ECh. 6.3 - Using the Trapezoidal Rule and Simpsons Rule In...Ch. 6.3 - Prob. 11ECh. 6.3 - Prob. 12ECh. 6.3 - Prob. 13ECh. 6.3 - Prob. 14ECh. 6.3 - Prob. 15ECh. 6.3 - Prob. 16ECh. 6.3 - Prob. 17ECh. 6.3 - Prob. 18ECh. 6.3 - Prob. 19ECh. 6.3 - Prob. 20ECh. 6.3 - Prob. 31ECh. 6.3 - Prob. 32ECh. 6.3 - Prob. 33ECh. 6.3 - Prob. 34ECh. 6.3 - Prob. 35ECh. 6.3 - Prob. 36ECh. 6.3 - Prob. 37ECh. 6.3 - Prob. 38ECh. 6.3 - Prob. 39ECh. 6.3 - Error Analysis In Exercises 37-40, use the error...Ch. 6.3 - Prob. 43ECh. 6.3 - Electricity The table shows the residential prices...Ch. 6.3 - Prob. 45ECh. 6.3 - Prob. 46ECh. 6.3 - Prob. 47ECh. 6.3 - Prob. 48ECh. 6.4 - Prob. 1CPCh. 6.4 - Prob. 2CPCh. 6.4 - Prob. 3CPCh. 6.4 - Prob. 4CPCh. 6.4 - Prob. 5CPCh. 6.4 - Prob. 1SWUCh. 6.4 - Prob. 2SWUCh. 6.4 - Prob. 3SWUCh. 6.4 - Prob. 4SWUCh. 6.4 - Prob. 5SWUCh. 6.4 - Prob. 6SWUCh. 6.4 - Prob. 7SWUCh. 6.4 - Prob. 8SWUCh. 6.4 - Prob. 9SWUCh. 6.4 - Prob. 10SWUCh. 6.4 - Prob. 1ECh. 6.4 - Prob. 2ECh. 6.4 - Prob. 3ECh. 6.4 - Prob. 4ECh. 6.4 - Prob. 5ECh. 6.4 - Prob. 6ECh. 6.4 - Prob. 7ECh. 6.4 - Prob. 8ECh. 6.4 - Prob. 9ECh. 6.4 - Prob. 10ECh. 6.4 - Prob. 11ECh. 6.4 - Prob. 12ECh. 6.4 - Prob. 13ECh. 6.4 - Prob. 14ECh. 6.4 - Prob. 15ECh. 6.4 - Prob. 16ECh. 6.4 - Prob. 17ECh. 6.4 - Prob. 18ECh. 6.4 - Prob. 19ECh. 6.4 - Prob. 20ECh. 6.4 - Prob. 21ECh. 6.4 - Prob. 22ECh. 6.4 - Prob. 23ECh. 6.4 - Prob. 24ECh. 6.4 - Prob. 25ECh. 6.4 - Prob. 26ECh. 6.4 - Womens Height The mean height of American women...Ch. 6.4 - Prob. 28ECh. 6.4 - Quality Control A company manufactures wooden...Ch. 6.4 - Prob. 30ECh. 6.4 - Prob. 31ECh. 6.4 - Prob. 32ECh. 6.4 - Prob. 33ECh. 6.4 - Prob. 34ECh. 6.4 - Prob. 35ECh. 6.4 - Prob. 36ECh. 6.4 - Prob. 37ECh. 6.4 - Prob. 38ECh. 6.4 - Prob. 39ECh. 6.4 - Prob. 40ECh. 6.4 - Prob. 41ECh. 6.4 - Prob. 42ECh. 6 - Prob. 1RECh. 6 - Prob. 2RECh. 6 - Prob. 3RECh. 6 - Prob. 4RECh. 6 - Prob. 5RECh. 6 - Prob. 6RECh. 6 - Prob. 7RECh. 6 - Prob. 8RECh. 6 - Prob. 9RECh. 6 - Prob. 10RECh. 6 - Prob. 11RECh. 6 - Prob. 12RECh. 6 - Prob. 13RECh. 6 - Prob. 14RECh. 6 - Finding Present Value In Exercises 1316, find the...Ch. 6 - Prob. 16RECh. 6 - Prob. 17RECh. 6 - Prob. 18RECh. 6 - Prob. 19RECh. 6 - Prob. 20RECh. 6 - Prob. 21RECh. 6 - Prob. 22RECh. 6 - Prob. 23RECh. 6 - Prob. 24RECh. 6 - Prob. 25RECh. 6 - Prob. 26RECh. 6 - Prob. 27RECh. 6 - Prob. 28RECh. 6 - Prob. 29RECh. 6 - Prob. 30RECh. 6 - Prob. 31RECh. 6 - Prob. 32RECh. 6 - Prob. 33RECh. 6 - Prob. 34RECh. 6 - Prob. 35RECh. 6 - Prob. 36RECh. 6 - Prob. 37RECh. 6 - Prob. 38RECh. 6 - Prob. 39RECh. 6 - Prob. 40RECh. 6 - Prob. 41RECh. 6 - Prob. 42RECh. 6 - Prob. 43RECh. 6 - Prob. 44RECh. 6 - Prob. 45RECh. 6 - Prob. 46RECh. 6 - Prob. 47RECh. 6 - Prob. 48RECh. 6 - Prob. 49RECh. 6 - Prob. 50RECh. 6 - Prob. 51RECh. 6 - Prob. 52RECh. 6 - Prob. 53RECh. 6 - Prob. 54RECh. 6 - Prob. 55RECh. 6 - Prob. 56RECh. 6 - Prob. 57RECh. 6 - Prob. 58RECh. 6 - Prob. 59RECh. 6 - Prob. 60RECh. 6 - Endowment In Exercises 61 and 62, determine the...Ch. 6 - Prob. 62RECh. 6 - Prob. 63RECh. 6 - Prob. 64RECh. 6 - Prob. 1TYSCh. 6 - Prob. 2TYSCh. 6 - Prob. 3TYSCh. 6 - Prob. 4TYSCh. 6 - Prob. 5TYSCh. 6 - Prob. 6TYSCh. 6 - Prob. 7TYSCh. 6 - Prob. 8TYSCh. 6 - Prob. 9TYSCh. 6 - Prob. 10TYSCh. 6 - Prob. 11TYSCh. 6 - Prob. 12TYSCh. 6 - Prob. 13TYSCh. 6 - Prob. 14TYSCh. 6 - Prob. 15TYSCh. 6 - Prob. 16TYSCh. 6 - Prob. 17TYSCh. 6 - Prob. 18TYS
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