Math

Discrete Mathematics With ApplicationsFor each of the algorithm segments in 6—19, assume that n is a positive integer. (a) Compute the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed. For simplicity, however, count only comparisons that occur within if then statements; ignore those implied by for-next loops. (b) Use the theorem on polynomial orders to find an order for the algorithm segment. 14. t : = 0 for i : = 1 to n s : = 0 for j : = 1 to i s : = s + a [ j ] next j t : = t + s 2 next iBuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 11.3, Problem 14ES

Textbook Problem

For each of the algorithm segments in 6—19, assume that *n *is a positive integer. (a) Compute the actual number of elementary operations (additions, subtractions, multiplications, divisions, and comparisons) that are performed when the algorithm segment is executed. For simplicity, however, count only comparisons that occur within if then statements; ignore those implied by for-next loops. (b) Use the theorem on polynomial orders to find an order for the algorithm segment.

14.
*n*
*i*
*j*
*i*

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 When necessary, round off answers to two decimal places. In Exercises1-6, find a the volume and b the surface a...

Mathematics: A Practical Odyssey

Express each area as indicated. Round each answer to the same number of significant digits as in the original q...

Mathematics For Machine Technology

In Exercises 9-12, let Z be the standard normal variable. Find z if z satisfies the given value. P(zZz)=.8444

Finite Mathematics for the Managerial, Life, and Social Sciences

In the table for single taxpayers, how were the figures 922.50 and 5156.25 arrived at?

Mathematical Excursions (MindTap Course List)

Expand each expression in Exercises 122. (y1y)2

Finite Mathematics

The partial derivatives ∂f∂x and ∂f∂y of the function f(x,y)=ln(xy+1).

Mathematical Applications for the Management, Life, and Social Sciences

Perform the indicated operations and simplify: 101235

Elementary Technical Mathematics

Add the following fractions and reduce to lowest terms. 56+1256+36_86=126=113__

Contemporary Mathematics for Business & Consumers

In Exercises 1-8, find the indicated limit by first plotting the graph of the function in a suitable viewing wi...

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

True or False:

Study Guide for Stewart's Multivariable Calculus, 8th

General: Roll Two Dice You roll two fair dice, a green one and a red one. (a) Are the outcomes on the dice inde...

Understanding Basic Statistics

For each set of sample outcomes below, use Formula 6.2 to construct the 95 confidence interval for estimating ,...

Essentials Of Statistics

For Problems 55-94, simplify each numerical expression. Objectives 7 69+1187+14

Intermediate Algebra

State a hypothesis that identifies a specific variable that causes some people to choose red as their favorite ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Consider the following data for two independent random samples taken from two normal populations. a. Compute th...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Using the Integral Test In Exercises 3-22, confirm that the Integral Test can be applied to the series. Then us...

Calculus: Early Transcendental Functions

Show the boxplot for the data in exercise 46. 46. Consider a sample with data values of 27, 25, 20, 15, 30, 34,...

Essentials Of Statistics For Business & Economics

Evaluate using partial fractions.
2 ln |x + 1| − 2 ln |x + 2| + C
ln |x + 1| + 3 ln |x + 2| + C
3 ln |x + 1| −...

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

Finding a Maclaurin Polynomial In Exercises 17-26, find the n th Maclaurin polynomial for the function. f(x)=si...

Calculus of a Single Variable

In Exercise 11-14, factor the expression. y23x+94

Calculus: An Applied Approach (MindTap Course List)

Determine whether the given vectors are orthogonal, parallel, or neither. 23. (a) a = 9, 3, b = 2, 6 (b) a = 4,...

Multivariable Calculus

Reminder Round all answers to two decimal places unless otherwise indicated. A Bald Eagle Murder Mystery At 3:0...

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

Find the exact value of each of the following. tan135

Trigonometry (MindTap Course List)

What is the lowest score in the following distribution?

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

Use the following steps to show that n=1(1)n1n=ln2 Let hn and sn be the partial sums of the harmonic and altern...

Single Variable Calculus: Early Transcendentals

Solve each absolute value equation for x. |x|+x=2

College Algebra (MindTap Course List)

Find (a) u.v (b) u.u (c) (b) (c)(d) (e) v(f) 2(g)(h)(i) (j) (d) (u.v)v (e) u.(3v) u= 3,4 v= 1,5

Calculus: Early Transcendental Functions (MindTap Course List)

Data were collected on the top 1000 financial advisers by Barrons. Merrill Lynch had 239 people on the list and...

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

Population The population density of a city is approximated by the model f(x,y)=4000e0.01(x2+y2) for the region...

Multivariable Calculus

Ref erring to the previous exercise, let x and y be waiting times on two independently selected days. Define a ...

Introduction To Statistics And Data Analysis

The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the result...

Probability and Statistics for Engineering and the Sciences

Suppose that G and G are abelian groups such that G=H1H2 and G=H1H2. If H1 is isomorphic to H1 and H2 is isomor...

Elements Of Modern Algebra

Finding the Equation of a Parabola Find an equation for the parabola that has its vertex at the origin and sati...

Precalculus: Mathematics for Calculus (Standalone Book)

Calculate SP (the sum of products of deviations) for the following scores. Note: Both means are decimal values,...

Statistics for The Behavioral Sciences (MindTap Course List)

Convert from radians to degrees. 10. 83

Single Variable Calculus: Early Transcendentals, Volume I

(a) Give a definition of an ellipse in terms of foci. (b) Write an equation for the ellipse with foci (c, 0) an...

Calculus: Early Transcendentals

Internet Advertising Several months ago, John O'Hagan investigated the effect on the popularity of OHaganBooks....

Applied Calculus

EXPLORING CONCEPTS Finding Functions Find differentiable functions f and g that satisfy the specified condition...

Calculus (MindTap Course List)

On what interval is the curve y=0xt2t2+t+2dt concave downward?

Calculus (MindTap Course List)

A recent survey at a major corporation found that employees who regularly participated in the company fitness p...

Research Methods for the Behavioral Sciences (MindTap Course List)

Use a calculator to find the length of the curve correct to four decimal places. If necessary, graph the curve ...

Single Variable Calculus

Solve the equations in Exercises 126. x4x2=6

Finite Mathematics and Applied Calculus (MindTap Course List)

In calculus, it can be shown that the largest possible volume for the inscribed right circular cylinder in Exer...

Elementary Geometry For College Students, 7e

Sketch the torus that results when the given circle of radius length 1 unit is revolved about the horizontal li...

Elementary Geometry for College Students

In Problems 3542 use the Laplace transform to solve the given equation. 42. 0tf()f(t)d=6t3

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

[T] The demand D (in millions of barrels) for oil in ail oil-rich country is given by the function D(p)=150(2.7...

Calculus Volume 1

[T] Use a computer algebra system to computer the Riemann sum, LN, for N = 10, 30, 50 for f(x)=11x2 on [1, 1].

Calculus Volume 2

XN (60, 9). Suppose that you form random samples of 25 from this distribution. Let X be the random variable of ...

Introductory Statistics

The U.S. Golf Association has instituted a ban on long and belly putters. This has caused a great deal of contr...

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