Math

Discrete Mathematics With ApplicationsIn 5 and 6, trace the action of the binary search algorithm (Algorithm 11.5.1) on the variables index, bot, top, mid, and the given values of x for the input array a [ 1 ] = Chia , a [ 2 ] = Doug , a [ 3 ] = Jan , a [ 4 ] = Jim , a [ 5 ] = Jose , a [ 6] = Mary , a [ 7 ] = Rob , a [ 8 ] = Roy , a [ 9 ] = Sue , a [ 1O ] = Usha , where alphabetical ordering is used to compare elements of the array. 5. a. x = Chia b. x = MaxBuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 11.5, Problem 5ES

Textbook Problem

In 5 and 6, trace the action of the binary search algorithm (Algorithm 11.5.1) on the variables *index, bot, top, mid, *and the given values of *x *for the input array

5. a.

b.

Discrete Mathematics With Applications

Show all chapter solutions

Ch. 11.1 - If f is a real-valued function of a real variable,...Ch. 11.1 - A point (x,y) lies on the graph of a real-valued...Ch. 11.1 - If a is any nonnegative real number, then the...Ch. 11.1 - Given a function f:RR and a real number M, the...Ch. 11.1 - Given a function f:RR , to prove that f is...Ch. 11.1 - Given a function f:RR , to prove that f is...Ch. 11.1 - The graph of a function f is shown below. a. Is...Ch. 11.1 - The graph of a function g is shown below. a. Is...Ch. 11.1 - Sketch the graphs of the power functions p1/3and...Ch. 11.1 - Sketch the graphs of the power functions p3 and p4...

Ch. 11.1 - Sketch the graphs of y=2x and y=2x for each real...Ch. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - Sketch a graph for each of the functions defined...Ch. 11.1 - In each of 10—13 a function is defined on a set of...Ch. 11.1 - In each of 10—13 a function is defined on a set of...Ch. 11.1 - In each of 10—13 a function is defined on a set of...Ch. 11.1 - In each of 10—13 a function is defined on a set of...Ch. 11.1 - The graph of a function f is shown below. Find the...Ch. 11.1 - Show that the function f:RR defined by the formula...Ch. 11.1 - Show that the function g:RR defined by the formula...Ch. 11.1 - Let h be the function from R to R defined by the...Ch. 11.1 - Let k:RR be the function defined by the formula...Ch. 11.1 - Show that if a function f:RRis increasing, then f...Ch. 11.1 - Given real-valued functions f and g with the same...Ch. 11.1 - a. Let m be any positive integer, and define...Ch. 11.1 - Let f be the function whose graph follows. Sketch...Ch. 11.1 - Let h be the function whose graph is shown below....Ch. 11.1 - Let f be a real-valued function of a real...Ch. 11.1 - Let f be a real-valued function of a real...Ch. 11.1 - Let f be a real-valued function of a real...Ch. 11.1 - In 27 and 28, functions f and g are defined. In...Ch. 11.1 - In 27 and 28, functions f and g are defined. In...Ch. 11.2 - A sentence of the form Ag(n)f(n) for every na...Ch. 11.2 - A sentence of the tirm “ 0f(n)Bg(n) for every nb ”...Ch. 11.2 - A sentence of the form “ Ag(n)f(n)Bg(n)for every...Ch. 11.2 - When n1,n n2 and n2 n5__________.Ch. 11.2 - According to the theorem on polynomial orders, if...Ch. 11.2 - If n is a positive integer, then 1+2+3++n has...Ch. 11.2 - The following is a formal definition for ...Ch. 11.2 - The following is a formal definition for...Ch. 11.2 - The following is a formal definition for ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - In 4—9, express each statement using -, O-, or ...Ch. 11.2 - a. Show that for any integer n1,02n2+15n+421n2 ....Ch. 11.2 - a. Show that for any integer n1,023n4+8n2+4n35n4 ....Ch. 11.2 - a. Show that for any integer n1,07n3+10n2+320n3 ....Ch. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Use the definition of -notation to show that...Ch. 11.2 - Use the definition of -notation to show that n2is...Ch. 11.2 - Prove Theorem 11.2.7(b): If f and g are...Ch. 11.2 - Prove Theorem 11.2.1(b): If f and g are...Ch. 11.2 - Without using Theorem 11.2.4 prove that n5 is not...Ch. 11.2 - Prove Theorem 11.2.4: If f is a real-valued...Ch. 11.2 - a. Use one of the methods of Example 11.2.4 to...Ch. 11.2 - a. Use one of the methods of Example 11.2.4 to...Ch. 11.2 - a. Use one of the methods of Example 11.2.4 to...Ch. 11.2 - Suppose P(n)=amnm+am1nm1++a2n2+a1n+a0 , where all...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Use the theorem on polynomial orders to prove each...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - Prove each of the statements in 32—39. Use the...Ch. 11.2 - a. Prove: If c is a positive real number and if f...Ch. 11.2 - Prove: If c is a positive real number and...Ch. 11.2 - What can you say about a function f with the...Ch. 11.2 - Use Theorems 11.2.5-11.2.9 and the results of...Ch. 11.2 - Use Theorems 11.2.5-11.2.9 and the results of...Ch. 11.2 - Use Theorems 11.2.5-11.2.9 and the results of...Ch. 11.2 - a. Use mathematical induction to prove that if n...Ch. 11.2 - a. Let x be any positive real number. Use...Ch. 11.2 - Prove Theorem 11.2.6(b): If f and g are...Ch. 11.2 - Prove Theorem 11.2.7(a): If f is a real-valued...Ch. 11.2 - Prove Theorem 11.2.8: a. Let f and g be...Ch. 11.2 - Prove Theorem 11.2.9: a. Let f1,f2 , and g be...Ch. 11.3 - When an algorithm segment contains a nested...Ch. 11.3 - In the worst case for an input array of length n,...Ch. 11.3 - The worst-case order of the insertion sort...Ch. 11.3 - Suppose a computer takes 1 nanosecond ( =109...Ch. 11.3 - Suppose an algorithm requires cn2operations when...Ch. 11.3 - Suppose an algorithm requires cn3operations when...Ch. 11.3 - Exercises 4—5 explore the fact that for relatively...Ch. 11.3 - Exercises 4—5 explore the fact that for relatively...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - For each of the algorithm segments in 6—19, assume...Ch. 11.3 - Construct a table showing the result of each step...Ch. 11.3 - Construct a table showing the result of each step...Ch. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - Construct a trace table showing the action of...Ch. 11.3 - How many comparisons between values of a[j] and x...Ch. 11.3 - How many comparisons between values of a[j] and x...Ch. 11.3 - According to Example 11.3.6. the maximum number of...Ch. 11.3 - Consider the recurrence relation that arose in...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 28—35 refer to selection sort, which is...Ch. 11.3 - Exercises 36—39 refer to the following algorithm...Ch. 11.3 - Exercises 36—39 refer to the following algorithm...Ch. 11.3 - Exercises 36—39 refer to the following algorithm...Ch. 11.3 - Exercises 36—39 refer to the following algorithm...Ch. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.3 - Exercises 40—43 refer to another algorithm, known...Ch. 11.4 - The domain of any exponential function is , and...Ch. 11.4 - The domain of any logarithmic function is and its...Ch. 11.4 - If k is an integer and 2kx2k+1 then...Ch. 11.4 - If b is a real number with b1 , then there is a...Ch. 11.4 - If n is a positive integer, then 1+12+13++1nhas...Ch. 11.4 - Graph each function defined in 1-8. 1. f(x)=3x for...Ch. 11.4 - Graph each function defined in 1—8. 2. g(x)=(13)x...Ch. 11.4 - Graph each function defined in 1—8. 3. h(x)=log10x...Ch. 11.4 - Graph each function defined in 1—8. 4. k(x)=log2x...Ch. 11.4 - Graph each function defined in 1—8. 5. F(x)=log2x...Ch. 11.4 - Graph each function defined in 1—8. 6. G(x)=log2x...Ch. 11.4 - Graph each function defined in 1—8. 7. H(x)=xlog2x...Ch. 11.4 - Graph each function defined in 1—8. 8....Ch. 11.4 - The scale of the graph shown in Figure 11.4.1 is...Ch. 11.4 - a. Use the definition of logarithm to show that...Ch. 11.4 - Let b1 . a. Use the fact that u=logbvv=bu to show...Ch. 11.4 - Give a graphical interpretation for property...Ch. 11.4 - Suppose a positive real number x satisfies the...Ch. 11.4 - a. Prove that if x is a positive real number and k...Ch. 11.4 - If n is an odd integer and n1 ,is log2(n1)=log2(n)...Ch. 11.4 - If, n is an odd integer and n1 , is...Ch. 11.4 - If n is an odd integer and n1 , is...Ch. 11.4 - In 18 and 19, indicate how many binary digits are...Ch. 11.4 - In 18 and 19, indicate how many binary digits are...Ch. 11.4 - It was shown in the text that the number of binary...Ch. 11.4 - In each of 21 and 22, a sequence is specified by a...Ch. 11.4 - In each of 21 and 22, a sequence is specified by a...Ch. 11.4 - Define a sequence c1,c2,c3,recursively as follows:...Ch. 11.4 - Use strong mathematical induction to show that for...Ch. 11.4 - Exercises 25 and 26 refer to properties 11.4.9 and...Ch. 11.4 - Exercises 25 and 26 refer to properties 11.4.9 and...Ch. 11.4 - Use Theorems 11.2.7-11.2.9 and properties 11.4.11,...Ch. 11.4 - Use Theorems 11.2.7-11.2.9 and properties 11.4.11,...Ch. 11.4 - Use Theorems 11.2.7—11.2.9 and properties 11.4.11,...Ch. 11.4 - Use Theorems 11.2.7—11.2.9 and properties 11.4.11,...Ch. 11.4 - Show that 4n is not O(2n) .Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Prove each of the statements in 32—37, assuming n...Ch. 11.4 - Quantities of the form k1n+k2nlognfor positive...Ch. 11.4 - Calculate the values of the harmonic sums...Ch. 11.4 - Use part (d) of Example 11.4.7 to show that...Ch. 11.4 - Show that log2n is (log2n) .Ch. 11.4 - Show that log2n is (log2n) .Ch. 11.4 - Prove by mathematical induction that n10n for...Ch. 11.4 - Prove by mathematical induction that log2nn for...Ch. 11.4 - Show that if n is a variable that takes positive...Ch. 11.4 - Let n be a variable that takes positive integer...Ch. 11.4 - For each positive real number u,log2uuUse this...Ch. 11.4 - Use the result of exercise 47 above to prove the...Ch. 11.4 - Exercises 49 and 50 use L’Hôpital’s rule from...Ch. 11.4 - Exercises 49 and 50 use L’Hôpital’s rule from...Ch. 11.4 - Complete the proof in Example 11.4.4.Ch. 11.5 - To solve a problem using a divide-and-conquer...Ch. 11.5 - To search an array using the binary search...Ch. 11.5 - The worst-case order of the binary search...Ch. 11.5 - To sort an array using the merge sort algorithm,...Ch. 11.5 - The worst-case order of the merge sort algorithm...Ch. 11.5 - Use the facts that log2103.32 and that for each...Ch. 11.5 - Suppose an algorithm requires clog2n operations...Ch. 11.5 - Exercises 3 and 4 illustrate that for relatively...Ch. 11.5 - Exercises 3 and 4 illustrate that for relatively...Ch. 11.5 - In 5 and 6, trace the action of the binary search...Ch. 11.5 - In 5 and 6, trace the action of the binary search...Ch. 11.5 - Suppose bot and top are positive integers with...Ch. 11.5 - Exercises 8—11 refer to the following algorithm...Ch. 11.5 - Exercises 8—11 refer to the following algorithm...Ch. 11.5 - Exercises 8—11 refer to the following algorithm...Ch. 11.5 - Exercises 8—11 refer to the following algorithm...Ch. 11.5 - Exercises 12—15 refer to the following algorithm...Ch. 11.5 - Exercises 12—15 refer to the following algorithm...Ch. 11.5 - Exercises 12—15 refer to the following algorithm...Ch. 11.5 - Exercises 12—15 refer to the following algorithm...Ch. 11.5 - Complete the proof of case 2 of the strong...Ch. 11.5 - Trace the modified binary search algorithm for the...Ch. 11.5 - Suppose an array of length k is input to the while...Ch. 11.5 - Let wnbe the number of iterations of the while...Ch. 11.5 - In 20 and 21, draw a diagram like Figure 11.5.4 to...Ch. 11.5 - In 20 and 21, draw a diagram like Figure 11.5.4 to...Ch. 11.5 - In 22 and 23, draw a diagram like Figure 11.5.5 to...Ch. 11.5 - In 22 and 23, draw a diagram like Figure 11.5.5 to...Ch. 11.5 - Show that given an array a[bot],a[bot+1],,a[top]of...Ch. 11.5 - The recurrence relation for m1,m2,m3,,which arises...Ch. 11.5 - It might seem that n1 multiplications are needed...

Find more solutions based on key concepts

Show solutions The problems in Exercises 6182 correspond to those in Exercises 2344, Section 2.1. Use the results of your prev...

Finite Mathematics for the Managerial, Life, and Social Sciences

Perform the indicated operations and simplify: 5lb3oz=oz

Elementary Technical Mathematics

Convert the given base ten numeral to the indicated base. 394 to base sixteen

Mathematical Excursions (MindTap Course List)

Calculate each expression in Exercises 124, giving the answer as a whole number or a fraction in lowest terms. ...

Finite Mathematics

Solve each of the following equations using the root principle of equality. Round the answers to 3 decimal plac...

Mathematics For Machine Technology

39. Production A small industry produces two items, I and II. It operates at capacity and makes a profit of $18...

Mathematical Applications for the Management, Life, and Social Sciences

The weight, in pounds, of thirty-five packages of ground beef at the Cut Above Market were as follows: 1.0 1.9 ...

Mathematics: A Practical Odyssey

For problems 27-54, simplify each of the numerical expressions. Objective 2 and 3 2(3)22(2)36(1)5

Intermediate Algebra

Methods 1. The response to a question has three alternatives: A, B, and C. A sample of 120 responses provides 6...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

At St. Algebra College, the 200 freshmen enrolled in introductory biology took a final exam on which their mean...

Essentials Of Statistics

Higher-Order DifferentiationIn Exercises 2326, find (a) r(t), (b) r(t), and (c) r(t)r(t), and (d) r(t)r(t). r(t...

Multivariable Calculus

Factoring by Grouping Factor the expression by grouping terms. 90. x5 + x4 + x + 1

Precalculus: Mathematics for Calculus (Standalone Book)

The article Americans Say No to Electric Cars Despite Gas Prices (USA TODAY, May 25, 2011) describes a survey o...

Introduction To Statistics And Data Analysis

Give (a) the point-slope form, (b) the slope-intercept form, and (c) the general form of an equation of a line.

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

In Exercises 11 and12, make drawings as needed. Suppose that for ABC and MNQ, you know that AM and BN. Explain ...

Elementary Geometry For College Students, 7e

In working further with the problem of exercise 4, statisticians suggested the use of the following curvilinear...

Statistics for Business & Economics, Revised (MindTap Course List)

For which positive integers k is the following series convergent? n=1(n!)2(kn)!

Multivariable Calculus

Evaluate the line integral. 6. C xy dx + ey dy + xz dz, C is given by r(t) = t4 i + t2 j + t3 k, 0 t 1

Calculus: Early Transcendentals

Archaeology: Artifacts Data for this problem are based on information taken from Prehistoric New Mexico: Backgr...

Understanding Basic Statistics

In Exercises 17 to 22, draw an ideally placed figure in the coordinate system; then name the coordinates of eac...

Elementary Geometry for College Students

Prove that is irreducible over for any prime. (Hint: Note that and consider. Use Binomial Theorem and Eisen...

Elements Of Modern Algebra

True or False: The domain is all numbers x for which f(x) is defined.

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

58 Find the area of the shaded region. r=ln, 12

Calculus (MindTap Course List)

Use elimination to solve {x+2y=22xy=6

College Algebra (MindTap Course List)

Tangent Line Let P(5,12) be a point on the circle x2+y2=169 (see figure). (a) What is the slope of the line joi...

Calculus of a Single Variable

33. Laurie Carron borrowed $16,000 at 14% ordinary interest for 88 days. On day 30 of the loan, she made a part...

Contemporary Mathematics for Business & Consumers

Finding an Indefinite Integral In Exercises 39-48, find the indefinite integral. sin2xcos2xdx

Calculus

State whether each of the following graphs represents a function.

Trigonometry (MindTap Course List)

(a) Evaluate the integral 0xnexdx for n = 0, 1, 2, and 3. (b) Guess the value of 0xnexdx when n is an arbitrary...

Single Variable Calculus: Early Transcendentals

Let a=log2,b=log3, and c=log7. In Exercises 2946, use the logarithm identities to express the given quantity in...

Applied Calculus

Polar-to-Rectangular Conversion In Exercises 73-78, convert the polar equation to rectangular form and sketch i...

Calculus: Early Transcendental Functions (MindTap Course List)

Trigonometric Functions Find sin , cos , and tan .

Calculus: Early Transcendental Functions

A researcher evaluates a new cholesterol medication by measuring cholesterol levels for a group of patients bef...

Research Methods for the Behavioral Sciences (MindTap Course List)

Function Value from Initial Value and Growth Factor Suppose that f is an exponential function with decay factor...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

By any method, determine all possible real solutions of each equation in Exercises 1330. Check your answers by ...

Finite Mathematics and Applied Calculus (MindTap Course List)

47. A financial manager made two new investments—one in the oil industry and one in municipal bonds. After a on...

Essentials Of Statistics For Business & Economics

Finding Parametric EquationsIn Exercises 1724, find a set of parametric equations of the line with the given ch...

Calculus (MindTap Course List)

Describe the process of simple random sampling, recognize this technique when it appears in a research report, ...

Research Methods for the Behavioral Sciences (MindTap Course List)

The joint pdf of pressures for right and left front tires is given in Exercise 9. a. Determine the conditional ...

Probability and Statistics for Engineering and the Sciences

In Exercises 3-6, simplify the expression. (14)x3/4

Calculus: An Applied Approach (MindTap Course List)

Which vector at the right could be a gradient for f(x, y)?
a
b
c
d

Study Guide for Stewart's Multivariable Calculus, 8th

Boyles Law states that when a sample of gas is compressed at a constant temperature, the pressure P of the gas ...

Single Variable Calculus: Early Transcendentals, Volume I

Produce graphs of f that reveal all the important aspects of the curve. Use graphs of f and f to estimate the i...

Single Variable Calculus

The spotlight effect refers to overestimating the extent to which others notice your appearance or behaviour, e...

Statistics for The Behavioral Sciences (MindTap Course List)

Describe what is measured by the estimated standard error in the bottom of the independent-measures t statistic...

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

In Problems 2130 use the Laplace transform to solve the given initial-value problem. 23. y + 2y + y = 0, y(0) =...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

[T] In the following exercises, set up a table of values and round to eight significant digits. Based on the ta...

Calculus Volume 1

Suppose that for each i such that 1iN one has i1if(t)dt=i2 . Show that 0Nf(t)dt=N( N+1)( 2N+1)6 .

Calculus Volume 2

For each probability and percentile problem, draw the picture When age is rounded to the nearest year, do the d...

Introductory Statistics

Restricting the Domain In Exercises 71-78, restrict the domain of the function f so that the function is one-to...

College Algebra

Price Comparison of Smoothie Blenders. A personal fitness company produces both a deluxe and a standard model o...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)