Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
13th Edition
ISBN: 9780321869838
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter B.3, Problem 18E
In Problems 1–20, evaluate each expression.
18. 5C5
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
7.
Define the sequence {b} by
bo = 0
Ել ։
= 2
8.
bn=4bn-1-4bn-2 for n ≥ 2
(a) Give the first five terms of this sequence.
(b) Prove: For all n = N, bn = 2nn.
Let a Rsuch that a 1, and let nЄ N. We're going to derive a formula for
Σoa without needing to prove it by induction. Tip: it can be helpful to use C1+C2+...+Cn
notation instead of summation notation when working this out on scratch paper.
(a) Take a a² and manipulate it until it is in the form Σ.a.
i=0
(b) Using this, calculate the difference between a Σ0 a² and Σ0 a², simplifying away the
summation notation.
i=0
(c) Now that you know what (a – 1) Σ0 a² equals, divide both sides by a − 1 to derive the
formula for
a².
(d) (Optional, just for induction practice) Prove this formula using induction.
3.
Let A, B, and C be sets and let f: A B and g BC be functions. For
each of the following, draw arrow diagrams that illustrate the situation, and then prove the
proposition.
(a) If ƒ and g are injective, then go f is injective.
(b) If ƒ and g are surjective, then go f is surjective.
(c) If gof is injective then f is injective. Make sure your arrow diagram shows that 9 does
not need to be injective!
(d) If gof is surjective then g is surjective. Make sure your arrow diagram shows that f
does not need to be surjective!
4.
5.
6.
Let X be a set and let f: XX be a function. We say that f is an involution if
fof idx and that f is idempotent if f f = f.
(a) If f is an involution, must it be invertible? Why or why not?2
(b) If f is idempotent, must it be invertible? Why or why not?
(c) If f is idempotent and x E range(f), prove that f(x) = x.
Prove that [log3 536] 5. You proof must be verifiable by someone who does not
have access to a scientific calculator or a logarithm table (you cannot use log3 536≈ 5.7).
Define the sequence {a} by a = 2-i for i≥ 1.
(a) Give the first five terms of the sequence.
(b) Prove that the sequence is increasing.
Chapter B.3 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
Ch. B.3 - Evaluate. (A)4! (B)7!6! (C)8!5!Ch. B.3 - Find (A)5C2 (B)6C0Ch. B.3 - Use the binomial theorem to expand (x + 2)5.Ch. B.3 - Use the binomial theorem to find the fourth term...Ch. B.3 - In Problems 120, evaluate each expression. 1.6!Ch. B.3 - In Problems 120, evaluate each expression. 2.7!Ch. B.3 - In Problems 120, evaluate each expression. 3.10!9!Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - In Problems 120, evaluate each expression. 5.12!9!Ch. B.3 - In Problems 120, evaluate each expression. 6.10!6!
Ch. B.3 - Prob. 7ECh. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 9ECh. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 12ECh. B.3 - Prob. 13ECh. B.3 - In Problems 120, evaluate each expression. 14.7C3Ch. B.3 - In Problems 120, evaluate each expression. 15.6C5Ch. B.3 - Prob. 16ECh. B.3 - In Problems 120, evaluate each expression. 17.5C0Ch. B.3 - In Problems 120, evaluate each expression. 18.5C5Ch. B.3 - In Problems 120, evaluate each expression....Ch. B.3 - Prob. 20ECh. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Expand each expression in Problems 2126 using the...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Prob. 28ECh. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Find the indicated term in each expansion in...Ch. B.3 - Prob. 32ECh. B.3 - Show that nC0 = nCn for n 0.Ch. B.3 - Prob. 34ECh. B.3 - The triangle shown here is called Pascals...Ch. B.3 - Explain why the sum of the entries in each row of...Ch. B.3 - Explain why the alternating sum of the entries in...Ch. B.3 - Prob. 38ECh. B.3 - Show that nCr1+nCr=n+1Cr for n r 1.
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
- Practice Assignment 5.6 Rational Functions M Practice Assig Practice Assignment 5.6 Rational Functions Score: 120/150 Answered: 12/15 Question 10 A Write an equation for the function graphed below 5 + 4 1 2 H + + -7 -6 -5 -4 -3 -2 -1 2 34567 | -2 ర y = Question Help: Video Message instructor Post to forum Submit Questionarrow_forward1. 2. Define f: ZZ and 9: ZZ by f(x)=3x+1 and g(x) = x². (a) Calculate (go f)(2). (b) Find an explicit formula for the function gof. Define f: R2 R2 by f(x, y) = (3x+y, 5x+2y). Give an explicit formula for f-1. Verify that it is the inverse of f. Do not include a derivation for f¹ unless it is for the verification.arrow_forwardSuppose that two toothpaste companies compete for customers in a fixed market in which each customer uses either Brand A or Brand B. Suppose also that a market analysis shows that the buying habits of the customers fit the following pattern in the quarters that were analyzed: each quarter (three-month period), 30% of A users will switch to B, while the rest stay with A. Moreover, 40% of B users will switch to A in a given quarter, while the remaining B users will stay with B. Finally assume that this pattern does not vary from quarter to quarter. (a) If A initially has all of the customers, what are the market shares 2 quarters later? (b) If A initially has all of the customers, what are the market shares 20 quarters later? (c) If B initially has all of the customers, what are the market shares 2 quarters later? (d) If B initially has all of the customers, what are the market shares 20 quarters later?arrow_forward
- 1. The regular representation of a finite group G is a pair (Vreg, Dreg). Vreg is a vector space and Dreg is a homomorphism. (a) What is the dimension of Vreg? (b) Describe a basis for Vreg and give a formula for Dreg. Hence explain why the homo- morphism property is satisfied by Dreg. (c) Prove that the character ✗reg (g) defined by tr Dreg (g) is zero if g is not the identity element of the group. (d) A finite group of order 60 has five irreducible representations R1, R2, R3, R4, R5. R₁ is the trivial representation. R2, R3, R4 have dimensions (3,3,4) respectively. What is the dimension of R5? Explain how your solution is related to the decomposition of the regular representation as a direct sum of irreducible representations (You can assume without proof the properties of this decomposition which have been explained in class and in the lecture notes). (e) A group element has characters in the irreducible representations R2, R3, R4 given as R3 R2 (g) = -1 X³ (g) = −1 ; XR4 (g) = 0…arrow_forwardit's not algebra 4th gradearrow_forwardNot use ai pleasearrow_forward
- Find the complete set of values of the constant c for which the cubic equation 2x³-3x²-12x + c = 0 has three distinct real solutionsarrow_forwardCan you tell me if I answered and showed my work correctlyarrow_forwardLO 2 -5 -4 -3 -2 0 --1- 2 + -5 Which system is represented in the graph? + LO 5 Xarrow_forward
- > co LO -6 -5 -4 4 do 3 3 2 1 Τ O 1 3 4 5 --6- -CO 6arrow_forward3.12 (B). A horizontal beam AB is 4 m long and of constant flexural rigidity. It is rigidly built-in at the left-hand end A and simply supported on a non-yielding support at the right-hand end B. The beam carries Uniformly distributed vertical loading of 18 kN/m over its whole length, together with a vertical downward load of 10KN at 2.5 m from the end A. Sketch the S.F. and B.M. diagrams for the beam, indicating all main values. Cl. Struct. E.] CS.F. 45,10,376 KN, B.M. 186, +36.15 kNm.7arrow_forwardDraw the isoclines with their direction markers and sketch several solution curves, including the curve satisfying the given initial conditions. 1) y'=x + 2y ; y(0) = 1 and 2) y' = x², y(0)=1arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
Holt Mcdougal Larson Pre-algebra: Student Edition...
Algebra
ISBN:9780547587776
Author:HOLT MCDOUGAL
Publisher:HOLT MCDOUGAL
College Algebra (MindTap Course List)
Algebra
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:Cengage Learning
Algebra: Structure And Method, Book 1
Algebra
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:McDougal Littell
The Fundamental Counting Principle; Author: AlRichards314;https://www.youtube.com/watch?v=549eLWIu0Xk;License: Standard YouTube License, CC-BY
The Counting Principle; Author: Mathispower4u;https://www.youtube.com/watch?v=qJ7AYDmHVRE;License: Standard YouTube License, CC-BY