Math

Discrete Mathematics With ApplicationsExercises 40—43 refer to another algorithm, known as Horner’s rule, for finding the value of a polynomial. Algorithm 11.3.4 Homer’s Rule [This algorithn computes the value of a polynomial a [ n ] x n + a [ n − 1 ] x n − 1 + ⋯ + a [ 2 ] x 2 + a [ 1 ] x + a [ 0 ] by nesting successive additions and multiplications as indicated in the following parenthesization: ( ( ⋯ ( ( a [ n ] x + a [ n − 1 ] ) x + a [ n − 2 ] ) x + ⋯ + a [ 2 ] ) x + a [ 1 ] ) x + a [ 0 ] . At each stage, starting with a [ n ] , the current value of polyval is multiplied by x and the next lower coefficient of the polynomial is added to it.] Input: n[a nonnegative integer], a [ 0 ] , a [ 1 ] , a [ 2 ] , … , a [ n ] [an array of real numbers], x [a real number] Algorithm Body: p o l y v a l : = a [ n ] for i : = 1 to n p o l y v a l : = p o l y v a l ⋅ x + a [ n − i ] next i [ A t t h i s p o i n t p o l y v a l = a [ n ] x n + a [ n − 1 ] x n − 1 + ⋯ + a [ 2 ] x 2 + a [ 1 ] x + a [ 0 ] . ] Output: polyval [a real number] 40. Trace Algorithm 11.3.4 for the input n = 3 , a [ 0 ] = 2 , a [ 1 ] = 1 , a [ 2 ] = − 1 , a [ 3 ] = 3 , and x = 2 .BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 11.3, Problem 40ES

Textbook Problem

Exercises 40—43 refer to another algorithm, known as Horner’s rule, for finding the value of a polynomial.

Algorithm 11.3.4 Homer’s Rule *[This algorithn computes the value of a polynomial *
*by nesting successive additions and multiplications as indicated in the following parenthesization:*

*At each stage, starting with *
*the current value of polyval is multiplied by x and the next lower *coefficient *of the polynomial is added to it.]* Input: *n[a nonnegative integer], *
*[an array of real numbers], x [a real number]* Algorithm Body:

*n *
*i *

Output: *polyval [a real number]*

40. Trace Algorithm 11.3.4 for the input

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 Use the 1s complement method to subtract the following binary numbers. 10111001_

Elementary Technical Mathematics

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

Finite Mathematics

[Type here]
In Problems 42 and 43, use a graphing utility to graph each function. Find any turning points.
43....

Mathematical Applications for the Management, Life, and Social Sciences

In Exercises 33-54, solve the given equation. The solution of every other odd-numbered exercise is given in the...

Mathematics: A Practical Odyssey

Write each Egyptian numeral as a Hindu-Arabic numeral.

Mathematical Excursions (MindTap Course List)

A machinist's gross income is $875 a week. If the cost of living goes up 3.4%, how much must the gross income i...

Mathematics For Machine Technology

CYBER MONDAY SALES The amount in millions of dollars spent on Cyber Monday for the years 2009 through 2011 is g...

Finite Mathematics for the Managerial, Life, and Social Sciences

EXPLORING CONCEPTS Approximation In Exercises 53 and 54, determine which best approximates the definite integra...

Calculus (MindTap Course List)

In Exercises 516, evaluate the given quantity. log1,000

Applied Calculus

For Problems 55-94, simplify each numerical expression. Objectives 7 [14(1618)][32(89)]

Intermediate Algebra

Solve each system by the elimination method, if possible. 3x+4y+2z=46x-2y+z=43x-8y-6z=-3

College Algebra (MindTap Course List)

Exercises Determine wether the given figure has rotational symmetry or reflective symmetry.

Elements Of Modern Algebra

Convert the expressions in Exercises 6584 to power form. 8

Finite Mathematics and Applied Calculus (MindTap Course List)

For Problems 5-14, please provide the following information. (a) What is the level of significance? State the n...

Understanding Basic Statistics

Given: ABC; RS is the perpendicular bisector of AB; RT is theperpendicular bisector ofBC. Prove: ARRC

Elementary Geometry For College Students, 7e

For each of the following one-to-one functions, find the equation of the inverse. Write the inverse using the n...

Trigonometry (MindTap Course List)

SW The following essay questions review the basic principles and concepts of inferential statistics. The order ...

Essentials Of Statistics

Find the area of the region enclosed by the hyperbola x2/a2y2/b2=1 and the vertical line through a focus.

Calculus (MindTap Course List)

A recent study indicates that people tend to select video game avatars with characteristics similar to those of...

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

Home Equity When you purchase a home by securing a mortgage, the total paid toward the principle is your equity...

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

Find the volume of the largest circular cone that can be inscribed in a sphere of radius r.

Single Variable Calculus: Early Transcendentals, Volume I

For a sample with a standard deviation of s=8, a score of X=65 corresponds to z=1.50. What is the sample mean?

Statistics for The Behavioral Sciences (MindTap Course List)

Direction Angles of a Vector Two direction angles of a vector are given. Find the third direction angle, given ...

Precalculus: Mathematics for Calculus (Standalone Book)

Investment The value of an investment of $1000 earning 6% compounded annually is V(I,R)=10001+0.06(1R)1+I10 whe...

Calculus: Early Transcendental Functions (MindTap Course List)

Coterminal Angles Explain how to find coterminal angles in degrees.

Calculus of a Single Variable

14. Percentage are a way of expressing a change from an
original amount to a new amount without using a percent...

Contemporary Mathematics for Business & Consumers

Determine whether the series is convergent or divergent. 19. n=1n3n4+4

Single Variable Calculus

Writing an equation of a Line In Exercises 7174, find an equation of the line with the given characteristics. A...

Calculus: An Applied Approach (MindTap Course List)

Each of the following studies examines the relationship between sugar consumption and activity level for presch...

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine whether the series is convergent or divergent by expressing sn as a telescoping sum (as in Example 8)...

Multivariable Calculus

The length of the curve given by x = 3t2 + 2, y = 2t3, is:

Study Guide for Stewart's Multivariable Calculus, 8th

In Exercises 17 to 22, use a form of the Law of Sines to find the measure of the indicated side or angle. Angle...

Elementary Geometry for College Students

Suppose the probability distribution of x, the number of defective tires on a randomly selected car checked at ...

Introduction To Statistics And Data Analysis

A tax preparation firm is interested in comparing the quality of work at two of its regional offices. The obser...

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

The following list contains several variables that differentiate college students. a. Select two variables from...

Research Methods for the Behavioral Sciences (MindTap Course List)

Cell Phone Companies Customer Satisfaction. Consumer Reports provides overall customer satisfaction scores for ...

Essentials Of Statistics For Business & Economics

A sample of 10 NCAA college basketball game scores provided the following data. a. Compute the mean and standar...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Contamination of mine soils in China is a serious environmental problem. The article Heavy Metal Contamination ...

Probability and Statistics for Engineering and the Sciences

A hemispherical bubble is placed on a spherical bubble of radius 1. A smaller hemispherical bubble is then plac...

Calculus: Early Transcendentals

Finding Coordinates of a Point In Exercises 9-12, find the coordinates of the point. The point is located three...

Multivariable Calculus

Evaluate the integral. 26. xsinxcosxdx

Single Variable Calculus: Early Transcendentals

Proof Given two infinite series an and bn such that an converges and bn diverges, prove that (an+bn) diverges.

Calculus: Early Transcendental Functions

True or False: If f(x) = g(x) for all x then f(x) = g(x).

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

In Exercises 6372, evaluate the expression. 69. | 1| + 2

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

In the following exercises, evaluate the integral using area formulas. 82. 01236 ( x6 )2dx

Calculus Volume 2

In Problems 1926 solve the given differential equation. 21. (6x+1)y2dydx+3x2+2y3=0

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

For the following problems, evaluate the limit using the squeeze theorem. Use a calculator to graph the functio...

Calculus Volume 1

Show the five-number summary and the boxplot for the following data: 5, 15, 18, 10, 8, 12, 16, 10, 6.

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

Suppose X~ N(2, 6). What value of x has a z-score of three?

Introductory Statistics