Calculus: An Applied Approach (Providence College: MTH 109)
9th Edition
ISBN: 9781285142616
Author: Ron Larson
Publisher: CENGAGE C
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Chapter 6.1, Problem 43E
To determine
To calculate: The value of definite integral
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3. (i) Let A, B, C, D, E be positive constants. Find the limit
n³ D
lim A(BC)³ +1 en 4+E.
n→∞
[6 Marks]
(ii) Let X be a random variable with the standard normal distribution,
i.e. X has the probability density function
Let
1
f(x)
√2π
n3x2
Xn = 100(50 +X6) en³4, n = 1, 2,...,
3+1
(a) Find the limit lim∞ Xn, verify your answer.
Y = 100(50 +X) 22.
[6 Marks]
(b) Is Xn≤Y? Verify your answer.
[6 Marks]
(c) Is EY∞o? Verify your answer.
[6 Marks]
(d) Does lim∞ EXn
(e) Find lim∞ EXn.
Elim Xn? Why?
[6 Marks]
[3 Marks]
3. (i) Using the definition of the line integral of a vector field, calculate the
line integral
L³
F.dy
of the vector field F: R² → R² given by
F(x, y) = (y, x),
and where the curve & is the unit semi-circle centred at the origin, located in
the upper half-plane and oriented in the anticlockwise direction.
Hint. Represent the curve y as the join of two curves y = 71 + 1/2 (see Example 8.9
in the Notes).
[20 Marks]
(ii) Calculate the same integral using Green's Theorem.
[10 Marks]
1. Evaluate the integral
↓ f(x, y)dxdy,
of function f R² →R over the domain DC R2, where:
f(x, y) = 2x + y
and D is the is the triangle with vertices (0, -1), (1,0) and (0,2).
Hint. Represent D in the form D = {(x, y) = R² : x = (a, b), g(x) < y < h(x)} for
some a
Chapter 6 Solutions
Calculus: An Applied Approach (Providence College: MTH 109)
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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