EBK FINITE MATH AND APPLIED CALCULUS
7th Edition
ISBN: 8220103612005
Author: Costenoble
Publisher: CENGAGE L
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Chapter 7.1, Problem 76E
To determine
The explanation why the statement, “He plays soccer or rugby and cricket” is ambiguous.
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(7) (12 points) Let F(x, y, z) = (y, x+z cos yz, y cos yz).
Ꮖ
(a) (4 points) Show that V x F = 0.
(b) (4 points) Find a potential f for the vector field F.
(c) (4 points) Let S be a surface in R3 for which the Stokes' Theorem is valid. Use
Stokes' Theorem to calculate the line integral
Jos
F.ds;
as denotes the boundary of S. Explain your answer.
(3) (16 points) Consider
z = uv,
u = x+y,
v=x-y.
(a) (4 points) Express z in the form z = fog where g: R² R² and f: R² →
R.
(b) (4 points) Use the chain rule to calculate Vz = (2, 2). Show all intermediate
steps otherwise no credit.
(c) (4 points) Let S be the surface parametrized by
T(x, y) = (x, y, ƒ (g(x, y))
(x, y) = R².
Give a parametric description of the tangent plane to S at the point p = T(x, y).
(d) (4 points) Calculate the second Taylor polynomial Q(x, y) (i.e. the quadratic
approximation) of F = (fog) at a point (a, b). Verify that
Q(x,y) F(a+x,b+y).
=
(6) (8 points) Change the order of integration and evaluate
(z +4ry)drdy .
So S√ ²
0
Chapter 7 Solutions
EBK FINITE MATH AND APPLIED CALCULUS
Ch. 7.1 - Prob. 1ECh. 7.1 - Prob. 2ECh. 7.1 - Prob. 3ECh. 7.1 - Prob. 4ECh. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Prob. 7ECh. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Prob. 10E
Ch. 7.1 - Prob. 11ECh. 7.1 - Prob. 12ECh. 7.1 - Prob. 13ECh. 7.1 - Prob. 14ECh. 7.1 - Prob. 15ECh. 7.1 - Prob. 16ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 18ECh. 7.1 - In Exercises 1720, draw a Venn diagram that...Ch. 7.1 - Prob. 20ECh. 7.1 - Prob. 21ECh. 7.1 - Prob. 22ECh. 7.1 - Prob. 23ECh. 7.1 - Prob. 24ECh. 7.1 - Prob. 25ECh. 7.1 - Prob. 26ECh. 7.1 - Prob. 27ECh. 7.1 - Prob. 28ECh. 7.1 - Prob. 29ECh. 7.1 - Prob. 30ECh. 7.1 - Prob. 31ECh. 7.1 - Prob. 32ECh. 7.1 - Prob. 33ECh. 7.1 - Prob. 34ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 37ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 39ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 41ECh. 7.1 - In Exercises 3542, A={small,medium,large},...Ch. 7.1 - Prob. 43ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 7.1 - Prob. 45ECh. 7.1 - Let A={H, T} be the set of outcomes when a coin is...Ch. 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 - Prob. 53ECh. 7.1 - Prob. 54ECh. 7.1 - Prob. 55ECh. 7.1 - Prob. 56ECh. 7.1 - Prob. 57ECh. 7.1 - Prob. 58ECh. 7.1 - Prob. 59ECh. 7.1 - Prob. 60ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Prob. 66ECh. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - Databases A freelance computer consultant keeps a...Ch. 7.1 - You sell iPads and jPads. Let I be the set of all...Ch. 7.1 - Prob. 72ECh. 7.1 - You are searching online for techno music that is...Ch. 7.1 - Prob. 74ECh. 7.1 - Prob. 75ECh. 7.1 - Prob. 76ECh. 7.1 - Prob. 77ECh. 7.1 - Prob. 78ECh. 7.1 - Prob. 79ECh. 7.1 - Prob. 80ECh. 7.1 - Prob. 81ECh. 7.1 - Prob. 82ECh. 7.1 - When this book was being written, the copy editor...Ch. 7.1 - Prob. 84ECh. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Let A={Drink,Johan,Frans,Sarie},...Ch. 7.2 - Verify that n(AB)=n(A)+n(B)n(AB) with A and B as...Ch. 7.2 - Verify that n(AC)=n(A)+n(C)n(AC) with A and C as...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - Let A={H,T},B={1,2,3,4,5,6}, and...Ch. 7.2 - If n(A)=43,n(B)=20, and n(AB)=3, find n(AB).Ch. 7.2 - If n(A)=60, n(B)=20, and n(AB)=1 find n(AB).Ch. 7.2 - If n(AB)=100andn(A)=n(B)=60, fi0nd n(AB).Ch. 7.2 - If n(A)=100,n(AB)=150, and n(AB)=40, find n(B).Ch. 7.2 - Prob. 19ECh. 7.2 - Prob. 20ECh. 7.2 - Prob. 21ECh. 7.2 - Prob. 22ECh. 7.2 - Prob. 23ECh. 7.2 - Prob. 24ECh. 7.2 - Prob. 25ECh. 7.2 - With S,A,andB as above, verify that...Ch. 7.2 - Prob. 27ECh. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - In Exercises 2730, use the given information to...Ch. 7.2 - Prob. 30ECh. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Web Searches In November 2011 a search using the...Ch. 7.2 - Amusement On a particularly boring transatlantic...Ch. 7.2 - Restaurant Menus While scanning through the...Ch. 7.2 - Mobile Gamers Of a total of 132 million mobile...Ch. 7.2 - Mobile Gamers Of a total of 208 million mobile...Ch. 7.2 - Prob. 37ECh. 7.2 - Prob. 38ECh. 7.2 - Prob. 39ECh. 7.2 - Prob. 40ECh. 7.2 - Prob. 41ECh. 7.2 - Prob. 42ECh. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Housing Starts Exercises 4348 are based on the...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Stocks Exercises 4954 are based on the following...Ch. 7.2 - Medicine In a study of Tibetan children,10 a total...Ch. 7.2 - Medicine In a study of Tibetan children,11 a total...Ch. 7.2 - Entertainment According to a survey of 100 people...Ch. 7.2 - Athletics Of the 4,700 students at Medium Suburban...Ch. 7.2 - Entertainment In a survey of 100 Enormous State...Ch. 7.2 - Entertainment Refer back to Exercise 59. You are...Ch. 7.2 - Prob. 61ECh. 7.2 - Prob. 62ECh. 7.2 - Why is the Cartesian product referred to as a...Ch. 7.2 - Refer back to your answer to Exercise 63. What set...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - Formulate an interesting application whose answer...Ch. 7.2 - When is n(AB)n(A)+n(B)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - When is n(AB)=n(A)?Ch. 7.2 - Use a Venn diagram or some other method to obtain...Ch. 7.2 - Prob. 72ECh. 7.3 - An experiment requires a choice among three...Ch. 7.3 - Prob. 2ECh. 7.3 - An experiment requires a sequence of three steps....Ch. 7.3 - Prob. 4ECh. 7.3 - Prob. 5ECh. 7.3 - Prob. 6ECh. 7.3 - Prob. 7ECh. 7.3 - Prob. 8ECh. 7.3 - Prob. 9ECh. 7.3 - Prob. 10ECh. 7.3 - Prob. 11ECh. 7.3 - Prob. 12ECh. 7.3 - How many different four-letter sequences can be...Ch. 7.3 - Prob. 14ECh. 7.3 - Ice Cream When Baskin-Robbins was founded in 1945,...Ch. 7.3 - Prob. 16ECh. 7.3 - Prob. 17ECh. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Ternary Codes A ternary digit is either 0, 1, or...Ch. 7.3 - Binary Codes A binary digit, or bit, is either 0...Ch. 7.3 - Reward While selecting candy for students in his...Ch. 7.3 - Productivity Professor Oger must choose between an...Ch. 7.3 - Prob. 23ECh. 7.3 - Radar Detectors Radar detectors are either powered...Ch. 7.3 - Multiple-Choice Tests Professor Easys final...Ch. 7.3 - Multiple-Choice Tests Professor Toughs final...Ch. 7.3 - Tests A test requires that you answer either Part...Ch. 7.3 - Tests A test requires that you answer first Part A...Ch. 7.3 - Stock Portfolios Your broker has suggested that...Ch. 7.3 - Prob. 30ECh. 7.3 - Computer Codes A computer byte consists of eight...Ch. 7.3 - Prob. 32ECh. 7.3 - Prob. 33ECh. 7.3 - Prob. 34ECh. 7.3 - Prob. 35ECh. 7.3 - Prob. 36ECh. 7.3 - Tournaments How many ways are there of filling in...Ch. 7.3 - Prob. 38ECh. 7.3 - Prob. 39ECh. 7.3 - Prob. 40ECh. 7.3 - Prob. 41ECh. 7.3 - Prob. 42ECh. 7.3 - DNA Chains: Life in Nature DNA (deoxyribonucleic...Ch. 7.3 - Prob. 44ECh. 7.3 - Prob. 45ECh. 7.3 - Telephone Numbers In the past, a local telephone...Ch. 7.3 - Romeo and Juliet Here is a list of the main...Ch. 7.3 - Prob. 48ECh. 7.3 - Prob. 49ECh. 7.3 - Prob. 50ECh. 7.3 - Mazes a. How many four-letter sequences are...Ch. 7.3 - Prob. 52ECh. 7.3 - Prob. 53ECh. 7.3 - Prob. 54ECh. 7.3 - Prob. 55ECh. 7.3 - Combination Locks Dripping wet after your shower,...Ch. 7.3 - Prob. 57ECh. 7.3 - Prob. 58ECh. 7.3 - Prob. 59ECh. 7.3 - Prob. 60ECh. 7.3 - Prob. 61ECh. 7.3 - Programming in Java Script (Some programming...Ch. 7.3 - Prob. 63ECh. 7.3 - Prob. 64ECh. 7.3 - Prob. 65ECh. 7.3 - Numbers How many odd numbers between 10 and 99...Ch. 7.3 - Prob. 67ECh. 7.3 - Prob. 68ECh. 7.3 - Prob. 69ECh. 7.3 - Prob. 70ECh. 7.3 - Prob. 71ECh. 7.3 - Find an interesting application that requires a...Ch. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 2ECh. 7.4 - Prob. 3ECh. 7.4 - In Exercises 116, evaluate the number. [HINT: See...Ch. 7.4 - Prob. 5ECh. 7.4 - Prob. 6ECh. 7.4 - Prob. 7ECh. 7.4 - Prob. 8ECh. 7.4 - Prob. 9ECh. 7.4 - Prob. 10ECh. 7.4 - Prob. 11ECh. 7.4 - Prob. 12ECh. 7.4 - Prob. 13ECh. 7.4 - Prob. 14ECh. 7.4 - Prob. 15ECh. 7.4 - Prob. 16ECh. 7.4 - How many ordered lists are there of four items...Ch. 7.4 - Prob. 18ECh. 7.4 - Prob. 19ECh. 7.4 - Prob. 20ECh. 7.4 - Prob. 21ECh. 7.4 - Prob. 22ECh. 7.4 - Prob. 23ECh. 7.4 - Prob. 24ECh. 7.4 - Prob. 25ECh. 7.4 - Prob. 26ECh. 7.4 - How many six-letter sequences are possible that...Ch. 7.4 - Prob. 28ECh. 7.4 - Prob. 29ECh. 7.4 - Prob. 30ECh. 7.4 - Prob. 31ECh. 7.4 - Prob. 32ECh. 7.4 - Prob. 33ECh. 7.4 - Prob. 34ECh. 7.4 - Prob. 35ECh. 7.4 - Marbles For Exercises 2942, a bag contains three...Ch. 7.4 - Prob. 37ECh. 7.4 - Prob. 38ECh. 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 - In Exercises 4752, calculate how many different...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 - Poker Hands A poker hand consists of 5 cards from...Ch. 7.4 - Prob. 56ECh. 7.4 - Prob. 57ECh. 7.4 - Prob. 58ECh. 7.4 - Prob. 59ECh. 7.4 - Prob. 60ECh. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Dogs of the Dow The Dogs of the Dow are the stocks...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Day Trading Day traders typically buy and sell...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 67ECh. 7.4 - Elimination Tournaments In an elimination...Ch. 7.4 - Prob. 69ECh. 7.4 - Prob. 70ECh. 7.4 - Prob. 71ECh. 7.4 - Prob. 72ECh. 7.4 - Prob. 73ECh. 7.4 - Prob. 74ECh. 7.4 - Prob. 75ECh. 7.4 - Prob. 76ECh. 7.4 - Prob. 77ECh. 7.4 - Prob. 78ECh. 7.4 - Prob. 79ECh. 7.4 - Prob. 80ECh. 7.4 - Prob. 81ECh. 7.4 - Prob. 82ECh. 7.4 - Prob. 83ECh. 7.4 - Prob. 84ECh. 7.4 - Prob. 85ECh. 7.4 - Prob. 86ECh. 7.4 - Prob. 87ECh. 7.4 - Complete the following: If a counting procedure...Ch. 7.4 - Prob. 89ECh. 7.4 - Prob. 90ECh. 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 - In Exercises 1924, consider a bag containing four...Ch. 7 - Prob. 20RECh. 7 - Prob. 21RECh. 7 - Prob. 22RECh. 7 - Prob. 23RECh. 7 - Prob. 24RECh. 7 - Prob. 25RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Prob. 27RECh. 7 - Inventories OHaganBooks.com currently operates...Ch. 7 - Inventories OHaganBooks.com currently operates...Ch. 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 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Online IDs As the customer base at OHaganBooks.com...Ch. 7 - Prob. 41RECh. 7 - Prob. 42RECh. 7 - Prob. 43RE
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