BuyFind*arrow_forward*

5th Edition

EPP + 1 other

Publisher: Cengage Learning,

ISBN: 9781337694193

Chapter 11.4, Problem 44ES

Textbook Problem

Prove by mathematical induction that

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 Explain why Benfords law would not apply to the set of telephone numbers in a small city such as Le Mars, Iowa.

Mathematical Excursions (MindTap Course List)

Simplify by first removing the parentheses and then combining the like terms: 0.45(x+3)0.75(2x+13)

Elementary Technical Mathematics

Divide:

Mathematical Applications for the Management, Life, and Social Sciences

MAXIMIZING INVESTMENT RETURNS Natsano has at most 50,000 to invest in the common stocks of two companies. He es...

Finite Mathematics for the Managerial, Life, and Social Sciences

In exercises 29-32, you are planning a survey for which the findings are to have the specified level of confide...

Mathematics: A Practical Odyssey

Solve each of the following equations using the multiplication principle of equality. Check each answer. 4=y(78...

Mathematics For Machine Technology

A company studied the number of lost-time accidents occurring at its Brownsville, Texas, plant. Historical reco...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Explain how a simple modification of the posttest-only nonequivalent control group design increases internal va...

Research Methods for the Behavioral Sciences (MindTap Course List)

Stock Market Performance. The Dow Jones Industrial Average (DJIA) and the Standard Poors 500 (SP 500) indexes ...

Essentials Of Statistics For Business & Economics

A long piece of galvanized sheet metal with width w is to be bent into a symmetric form with three straight sid...

Multivariable Calculus

Sometimes, Always, or Never: If f(x) is continuous on [a, b], then abf(x) dx exists.

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

Finding a Derivative In Exercises 41-56, find the derivative of the function. y=arctanx+x1+x2

Calculus

In Exercise 7 to 16, name the lines if any that must be parallel under the given conditions. 310

Elementary Geometry for College Students

Finding Perpendicular Lines Find the equation of the line perpendicular to y=3x+1 that passes through the point...

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

A researcher conducts an experiment comparing four treatment conditions with a separate sample of n=6 in each t...

Statistics for The Behavioral Sciences (MindTap Course List)

The area of a region D enclosed by a curve C, such as that pictured in question 1, may be evaluated using the l...

Study Guide for Stewart's Multivariable Calculus, 8th

A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoki...

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

Use your graphing calculator to graph each pair of functions together for 2x2. (Make sure your calculator is se...

Trigonometry (MindTap Course List)

Using Intercepts and Symmetry to Sketch a Graph In Exercises 9-14, find any intercepts and test for symmetry. T...

Calculus: Early Transcendental Functions

Using the Second Partials TestIn Exercises 720, examine the function for relative extrema and saddle points. h(...

Calculus: Early Transcendental Functions (MindTap Course List)

Find the ratio A1A2 of the areas of two similar rectangles if a the ratio of the lengths of the corresponding s...

Elementary Geometry For College Students, 7e

Data on x = poverty rate (%) and y = high school dropout rate (%) for the 50 U.S. states and the District of Co...

Introduction To Statistics And Data Analysis

For the following distribution of quiz scores, how many individuals took the quiz? x f 5 6 4 5 3 5 2 3 1 2 a. 5...

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

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

Applied Calculus

In a way, the central limit theorem can be thought of as a kind of grand central station. It is a connecting hu...

Understanding Basic Statistics

In Exercises 311, find the derivative of the function. f(x)=(3x2+4)2

Calculus: An Applied Approach (MindTap Course List)

PNTAM EXAM CHALLEG Suppose of f and g are non-constant, differentiable, real valued functions defined on (,) . ...

Calculus of a Single Variable

Exercises You can use the following problems as a self-test on the material presented in this review. If you ca...

Essentials Of Statistics

Proof Let F=Mi+Nj, where M and N have continuous first partial derivatives in a simply connected region R. Prov...

Multivariable Calculus

Explain why it can be useful to write a research proposal before conducting the actual research study.

Research Methods for the Behavioral Sciences (MindTap Course List)

Absolute Value Inequalities Solve the absolute value inequality. Express the answer using interval notation and...

Precalculus: Mathematics for Calculus (Standalone Book)

Estimate the horizontal asymptote of the function f(x)=3x3+500x2x3+500x2+100x+2000 by graphing .f for 10 x 10...

Single Variable Calculus: Early Transcendentals

Determining Absolute end Conditional Convergence In Exercises 41-58. determine whether the series converges abs...

Calculus (MindTap Course List)

Rewrite each expression in Exercises 116 as a single rational expression, simplified as much as possible. 2x3x2...

Finite Mathematics and Applied Calculus (MindTap Course List)

Compare the curves represented by the parametric equations. How do they differ? 37. (a) x = t3, y = t2 (b) x = ...

Calculus: Early Transcendentals

An individuals credit score is a number calculated based on that persons credit history that helps a lender det...

Probability and Statistics for Engineering and the Sciences

Find an equation of the tangent line to the curve at the given point. Illustrate by graphing the curve and the ...

Single Variable Calculus: Early Transcendentals, Volume I

True or False
Label each of the following statements as either true or false where represents a commutative rin...

Elements Of Modern Algebra

Let A=[2313], B=[215112], C=[216011], D=[1213], and E=[1223]. Verify each property by doing the operations on e...

College Algebra (MindTap Course List)

In Exercises 18, determine whether the equation defines y as a linear function of x. If so, write it in the for...

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

Give a step-by-step description of how you would use the ideas of this section to the graph f(x)=4x2+16x13.

Intermediate Algebra

Find the points on the ellipse x2+2y2=1 where the tangent line has slope 1.

Calculus (MindTap Course List)

At a recent boat show, Nautica Bank was offering boat loans for up to 5 years with an APR of 13.5%. On new boat...

Contemporary Mathematics for Business & Consumers

Graphs of f and g are shown. Decide whether each function is even, odd, or neither. Explain your reasoning. 69.

Single Variable Calculus

In Problems 4348 each figure represents the graph of a particular solution of one of the following differential...

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

For the following exercises, simplify each expression by writing it in terms of sines and cosines, then simplif...

Calculus Volume 1

For the following exercises, consider the catenoid, the only solid of revolution that has a minimal surface, or...

Calculus Volume 2

In recent years more people have been working past the age of 65. In 2005, 27% of people aged 65-69 worked. A r...

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