# INTRODUCTORY MATHEMATICAL ANALYSIS 13TH EDITION PDF

Introductory Mathematical Analysis for Business, Economics, and the Life and Social Sciences, International pixia-club.info - Ebook download as PDF File .pdf) or . Introductory Mathematical Analysis Textbook Solution Manual 13 edition - Ebook download as PDF File .pdf), Text File .txt) or read book online. quantative. Showing all editions for 'Introductory mathematical analysis: for business, . and the life and social sciences. by E Haeussler. Print book. English. 13th ed.

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Adding 9 — x to both sides and then dividing both sides by 2; equivalence guaranteed Introductory Mathematical Analysis 18 Thus there is no solution, so the solution set is C. The solution set is C. Introductory Mathematical Analysis 20 Thus there is no solution. Introductory Mathematical Analysis 22 By the Pythagorean theorem, 2 2 2 1. Let P be the amount in the account one year ago.

Then the interest earned is 0. Then the HST tax is 0. The percentage of the total that is HST is 0. Introductory Mathematical Analysis 24 9. Introductory Mathematical Analysis 26 Let 1. Introductory Mathematical Analysis 28 Let 2 1. Introductory Mathematical Analysis 30 The solution is —2.

If x —3, the equation is 3 1 5. Introductory Mathematical Analysis 32 Let l be the length of the picture, then its width is l — 2. The dimensions of the picture are 6 inches by 8 inches. This contradicts the restriction on v. Thus we choose 2 2 1 4 1.

When the object strikes the ground, h must be 0, so 2 0 By a program, roots are 4. By a program, roots are 1.

By a program, there are no real roots. The procedure works because multiplying a list by a number is the same as multiplying each element in the list by the number, adding a number to a list has the effect of adding the number to each element of the list, and subtracting one list from another is the same as subtracting corresponding elements. The plots match. The results agree.

Introductory Mathematical Analysis 34 4. The smaller quadratic residuals indicate a better fit. The fairly random pattern suggests that the model cannot be improved any further.

The slight deviations from the quadratic model are presumably due to random measurement errors. Let w be the width and 2w be the length of the plot.

Let w be the width and 2w be the length. The dimensions are 50 ft by ft. Then the remaining forest has dimensions 2 — 2w by 1 — 2w. Thus the width of the strip should be 1 4 mi. The remaining plot for flowers has dimensions 8 — 2w by 4 — 2w.

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Thus the width of the pavement should be 1 m. Since diameter of circular end is mm, the radius is 70 mm. Area of circular end is 2 2 radius Following the procedure in Example 6 we obtain the total value at the end of the second year to be 2 1, , 1. Following the procedure in Example 6 we obtain 2 2 3, , 1 3, , 1 1 1 2.

Introductory Mathematical Analysis Section 1. To triple an investment of P at the end of t years, the interest earned during that time must equal 2P. We equate incomes under both proposals. Let p be the percentage increase in market value. Then 1 1. Thus the dimensions are 80 ft by ft. The dimensions are 9 in.

Volume of old style candy 2 2 3 7. Considering the volume of the new style candy, we have 2 2 2 2 7. Hence, 0. Introductory Mathematical Analysis 40 We choose —32 36 The price of each acre sold was Then the revenue last year was 3q and this year it is 3.

By the definition of margin of profit, it follows that 0. Thus 15, units were sold last year and 17, this year. Each unit of B costs , q and each unit of A costs Thus the company produces either units of A and units of B, or units of A and units of B. Principles in Practice 1. Introductory Mathematical Analysis 42 If x is the measure of one acute angle, the other angle has measure 90 — x. Chapter 1: Introductory Mathematical Analysis 44 Let d be the number of disks.

Problems 1. We want Rental cost Purchase cost. Profit 0 3. Let q be the number of magazines printed. Then the cost of publication is 0.

The number of magazines sold is 0. The revenue from dealers is 0. If fewer than 30, magazines are sold, the only revenue is from the sales to dealers, while if more than 30, are sold, there are advertising revenues of 0. Thus, ISM: Let L be current liabilities. Introductory Mathematical Analysis 46 9. Introductory Mathematical Analysis 48 The solution is 1 3 ,. Let 1 T and 2 T be the temperatures of the two chemicals. The bounds of summation are 12 and 17; the index of summation is t.

The bounds of summation are 3 and ; the index of summation is m. Introductory Mathematical Analysis 50 Introductory Mathematical Analysis 52 By Equation 1.

Then p — 0. Let q units be produced at A and 10, — q at B. Then 3 3 3 4 12, 3 Both equations represent audio being written onto minute CDs. In the first equation, 18 hours minutes are being written to a CD using a combination of to-1 and to-1 compression ratios. Here, x gives the maximum amount of audio minutes or 10 hours that can be written using the to-1 compression ratio. In the second equation, A maximum of minutes can be written at to The formula for the area of a circle is 2 , r t where r is the radius.

The domain of a r is all real numbers. This can also be written as. The domain of t r is all real numbers except 0. Replacing r by x: Replacing r by: When the speed is reduced divided by a constant, the time is scaled multiplied by the same constant; Problems 2.

The functions are different because they have different domains. The functions are not equal because they have different domains. The functions are equal. Any other real number can be used for x. Introductory Mathematical Analysis Section 2. Any real number can be used for x. Any real number can be used for z. We exclude values of y for which 2 4 4 0. Functions and Graphs ISM: Introductory Mathematical Analysis 56 Introductory Mathematical Analysis 58 Thus y is a function of x.

Solving for x gives 9 4. Solving for x gives. Solving for x gives 2 1. Yes, because corresponding to each input r there is exactly one output, 2. After t weeks the excess accumulates to t. Depreciation at the end of t years is 0.

Yes; for each input q there corresponds exactly one output, 1. The dependent variable is P and the independent variable is q. The amount the coffee house supplies increases as the price increases. The premiums do not change regardless of the number of doctor visits. This is a constant function. The price for n pairs of socks is given by 3.

Chapter 2: Introductory Mathematical Analysis 60 4. Think of the bookshelf having 7 slots, from left to right. You have a choice of 7 books for the first slot. Once a book has been put in the first slot, you have 6 choices for which book to put in the second slot, etc. The cost for buying n tickets is 9. For a committee of four, there are 4 choices for who will be member A.

For each choice of member A, there are 3 choices for member G. Once members A and G have been chosen, there are two choices for member M, then one choice for member S once members A, G, and M have been chosen. Then l x represents the length of the sides of the square, while a x is the area of a square with side of length x. Introductory Mathematical Analysis 62 c. Introductory Mathematical Analysis 64 Then l x represents the length of the sides of the cube, while f x is the volume of a cube with sides of length x.

Principles in Practice 2. Therefore, after 12 months and approximately 2.

Introductory Mathematical Analysis 66 2. Since the line is parallel to the x-axis, there is no x-intercept. Therefore, we can represent the distance from the turn-around point at any time x as 30 —12x.

The monthly cost of x therms of gas is 0. So a real zero is —2. So a real zero is 2. So a real zero is 0. Not one-to-one. Thus there is no x-intercept. Introductory Mathematical Analysis 68 Because x cannot be 0, there is no y-intercept.

## Mathematics education

Because r 0, there is no vertical-axis intercept. Because t 0, there is no vertical-axis intercept. No intercepts Domain: Thus x 4. Introductory Mathematical Analysis 72 From the vertical-line test, the graphs that represent functions of x are a , b , and d. From the horizontal line test, the graphs which represent one-to-one functions of x are c and d. Therefore, Tara will have paid off her debt after 9 months. The cost of an item as a function of the time of day, x is A.

As price increases, quantity supplied increases; p is a function of q. As price decreases, quantity increases; p is a function of q. No real zeros Introductory Mathematical Analysis 74 Problems 2. Testing for symmetry gives: Since the graph has symmetry about x- and y-axes, there is also symmetry about the origin.

Introductory Mathematical Analysis 76 Testing for symmetry gives: Because f is not the zero function, there is no x-axis symmetry y-axis: Because f is not the zero function, there is no x-axis symmetry. Since there is symmetry about the x- and y-axes, symmetry about origin exists. Since there is symmetry about x- and y-axes, symmetry about origin exists. Since there is symmetry about x-and y-axes, symmetry about origin exists. Replacing x by —x gives 2 4 5 1. Introductory Mathematical Analysis 80 original equation.

Thus the graph is symmetric about the y-axis. Maximum value of f x: Thus the graph is symmetric about y-axis. Real zeros of f: Translate 3 units to the left, stretch vertically away from the x-axis by a factor of 2, reflect about the x-axis, and move 2 units upward.

Translate 3 units to the left and 4 units downward. Reflect about the y-axis and translate 5 units downward. Shrink horizontally toward the y-axis by a factor of 3. For x to be real, x must be nonnegative. For the denominator x — 1 to be different from 0, x cannot be 1. Both conditions are satisfied by all nonnegative numbers except 1. Introductory Mathematical Analysis Chapter 2 Review 83 b.

Introductory Mathematical Analysis 84 c. Introductory Mathematical Analysis Chapter 2 Review 85 y-axis: Introductory Mathematical Analysis 86 G u 10 u 10 S is a function of t. From the vertical-line test, the graphs that represent functions of x are a and c.

## If You're an Educator

Introductory Mathematical Analysis 88 4. Answers may vary. Then, In An equation relating the growth in enrollment to the number of years can be found by using the point-slope form of an equation of a line. A linear function relating Fahrenheit temperature to Celsius temperature can be found by using the point-slope form of an equation of a line.

C F — — To convert Celsius to Fahrenheit, locate the Celsius temperature on the horizontal axis, move vertically to the line, then move horizontally to read the Fahrenheit temperature of the vertical axis. Chapter 3: Introductory Mathematical Analysis 90 7. Right angles are formed by perpendicular lines. The slopes of the sides of the triangle are: Therefore, the points do not define a right triangle.

Problems 3. Introductory Mathematical Analysis Section 3. Introductory Mathematical Analysis 92 Thus the slope is undefined. There is no y-intercept. Introductory Mathematical Analysis 94 Thus they are parallel.

Both lines are vertical and thus parallel. The y-axis is vertical. Introductory Mathematical Analysis 96 The number of home runs hit increased as a function of time in months. Solve the equation for t. Using the points 3. Using the points 0. The slopes of the sides of the figure are: The path of descent is a straight line with a slope of —1 and y-intercept of The line has slope Thus C — The line has slope 50, and passes through 5, , Thus, the y-intercept is 7.

The slope is 7. Principles in Practice 3. Introductory Mathematical Analysis 98 3. Answers may vary, but two possible points are 0, 60 and 2, Since the height changes by 2. The points 0, 3 and 4, —5 lie on the graph of f. The points 1, 2 and —2, 8 lie on the graph of f.

The points 1, 1 and 2, 2 lie on the graph of f. The points —2, —1 and —4, —3 lie on the graph of f. Since f 0.

The points 40, The line passes through 26,, 12 and 10,, 18 , so 18 12 0. Introductory Mathematical Analysis The line passes through , and , , so 0. The points 50, 35 and 35, 30 lie on the graph of the equation, which is a line. The line passing through , 79 and , 88 has slope 88 79 0. Since The number of curative units from d cubic centimeters of the drug is d, and the number of curative units from r minutes of radiation is r. Each year the value decreases by 0.

After t years the total decrease is 0. The line has slope — and passes through 4, The line has slope 45, and passes through 5, , So 49, , Hence isoprofit lines are parallel. N R 5 0 Since c is the number of chirps per minute, then 1 4 c is the number of chirps in 1 4 minute or 15 seconds. Thus from part a , to estimate temperature add 37 to the number of chirps in 15 seconds. Thus, the vertex is 1, Thus the y-intercept is —6.

Thus the y-intercept is 5. Introductory Mathematical Analysis c. The maximum value is 2 20 4 20 50 0. The x-coordinate of the vertex Chapter 3: Thus, the vertex is 9, Since the total length of fencing is , the side opposite the highway has length — 2x.

Thus A is maximum when Thus the dimensions are ft by ft. Highway x x — 2x Let x, y be two numbers whose sum is Their product is then 2 78 Thus, two numbers whose sum is 78 and whose product is a maximum are 39 and Then, the problem states , , 0. Then, we have 4 2 , 5 7 Introductory Mathematical Analysis Thus 2 , Thus, the system of equations is 12 9 7 8. Substituting in Eq. From Eq. Introductory Mathematical Analysis 36 27 , 36 80 Thus 1 , 0.

Substitute these two values to solve for y: Then , 1 0. Then 0. Thus, the system of equations is 4 3 2 3. Now solve the system 0. Now convert the time into minutes and solve the system ISM: Thus we have the system 1. Therefore units of early American and units of Contemporary must be sold.

Then , 1 1. Substituting for x and z in Eq. Therefore liked, 80 disliked, and 40 had no comment. The total cost of Exton is 7. Thus 7. This gives the system , 1 7. Therefore calculators must be made at the Exton plant and calculators at the Whyton plant. Let x, y, and z be the amounts of 2.

Then , 1 2. Substituting for y in Eqs. Introductory Mathematical Analysis , 2. Substituting in the second equation gives 2. Then , 75, , 1 , , 14, A system that describes the situation is 25, , 0. Solving for 0. Then 8y clam-shells will be used. Let 1 p and 2 p be the amounts of the two investments, respectively. Since the percentage return on each was the same, and since interest rate amt.

Hence we have the system 1 2 1 1 2 3 , Wood used: Adding —2 times Eq. Thus chairs, rockers and chaise lounges should be made. Then 35, , 1 0. Then we have the system number of workers: Method 1.

Thus 25 Method 2. The number of minutes the pump on A operates is 25 a. For the pump on B, it is 35 b. Thus 5 1 25 35 10, Introductory Mathematical Analysis Problems 3. There are three solutions: There are two solutions: The system has four solutions: Thus there are two solutions: However, from Eq. But x cannot equal 1 in either of the original equations division by zero.

We can write the following system of equations. Introductory Mathematical Analysis The rope touches the streamer twice, 10 feet away from center on each side at —10, 7. The two holes are located at 10, The system has 3 solutions. Equating p-values gives 1 1 4 9 7 5 30, 5 The equilibrium point is 5 6 , 6. Equating p-values: The equilibrium point is 9, The equilibrium point is 6, But p cannot be negative. The equilibrium point is 15, 5.

Then Thus one cannot break even at any level of production. Subtracting Eq. The new total cost equation is TC 1. For the supply equation we fit the points 0, 1 and 13,, 4. We have 31 2 4. Let c be the variable cost per unit. Then at the break even point, Tot.

Thus total cost always exceeds total revenue; there is no break-even point.

After the subsidy the supply equation is 8 50 1. A general form: General form: Slope of a vertical line is undefined, so slope- intercept form does not exist. Slope of a horizontal line is 0. Introductory Mathematical Analysis Chapter 3 Review There is no solution. Thus, the equations are equivalent. From EQ. Let 1 p and 2 p be the prices in dollars of the two items, respectively, before the tax. At the time the difference in prices is 1 2 3. This gives the system 1 2 1 2 3.

Thus this scenario is not possible. The slope gives the change in R for each 1-unit increase in L. Thus the time necessary to travel from one level to the next level is 75 milliseconds. The points 32, 0 and , lie on the graph of the function. Equating L-values gives 0. The graph shows that 2 P and 3 P intersect when the second branch of 2 P crosses the first branch of 3.

## Frédo Durand

P Thus The graph shows that 3 P and 4 P intersect when the second branch of 3 P crosses the first branch of 4 P Thus The graph shows that 4 P and 5 P intersect when the second branch of 4 P crosses the first branch of 5 P Thus The graph shows that 5 P and 6 P intersect when the second branch of 5 P crosses the first branch of 6 P Thus No; answers may vary.

The shapes of the graphs are the same. The value of A scales the value of any point by A. Year Multiplicative Increase Expression 0 1 0 1. If we graph the multiplicative increase as a function of years we obtain the following.

This pattern will continue as shown in the table. Year Multiplicative Decrease Expression 0 1 0 0. If we graph the multiplicative decrease as a function of years, we obtain the following. Therefore, if 1. The interest earned over the first 5 years is Introductory Mathematical Analysis Section 4. Introductory Mathematical Analysis 8. For the curves, the bases involved are 0. For base 5, the curve rises from left to right, and in the first quadrant it rises faster than the curve for base 2.

Thus the graph is A. If we graph the multiplicative increase as function of years, we obtaining the following. Population of city A after 5 years: Population of city B after 5 years: Difference in populations: After 44 hours, approximately 1 4 of the initial amount remains.

Thus the half-life is approximately 22 hours. After one half-life, 1 2 gram remains. The first integer t for which the graph of 1. Using a graphics calculator, 0. Thus, 0. Principles in Practice 4. The product rule and chain rule , [14] the notions of higher derivatives and Taylor series , [15] and of analytic functions [ citation needed ] were introduced by Isaac Newton in an idiosyncratic notation which he used to solve problems of mathematical physics. In his works, Newton rephrased his ideas to suit the mathematical idiom of the time, replacing calculations with infinitesimals by equivalent geometrical arguments which were considered beyond reproach.

He used the methods of calculus to solve the problem of planetary motion, the shape of the surface of a rotating fluid, the oblateness of the earth, the motion of a weight sliding on a cycloid , and many other problems discussed in his Principia Mathematica In other work, he developed series expansions for functions, including fractional and irrational powers, and it was clear that he understood the principles of the Taylor series.

He did not publish all these discoveries, and at this time infinitesimal methods were still considered disreputable. Gottfried Wilhelm Leibniz was the first to state clearly the rules of calculus. These ideas were arranged into a true calculus of infinitesimals by Gottfried Wilhelm Leibniz , who was originally accused of plagiarism by Newton.

His contribution was to provide a clear set of rules for working with infinitesimal quantities, allowing the computation of second and higher derivatives, and providing the product rule and chain rule , in their differential and integral forms. Unlike Newton, Leibniz paid a lot of attention to the formalism, often spending days determining appropriate symbols for concepts. Today, Leibniz and Newton are usually both given credit for independently inventing and developing calculus.

Newton was the first to apply calculus to general physics and Leibniz developed much of the notation used in calculus today. The basic insights that both Newton and Leibniz provided were the laws of differentiation and integration, second and higher derivatives, and the notion of an approximating polynomial series. By Newton's time, the fundamental theorem of calculus was known. When Newton and Leibniz first published their results, there was great controversy over which mathematician and therefore which country deserved credit.

Newton derived his results first later to be published in his Method of Fluxions , but Leibniz published his " Nova Methodus pro Maximis et Minimis " first. Newton claimed Leibniz stole ideas from his unpublished notes, which Newton had shared with a few members of the Royal Society. This controversy divided English-speaking mathematicians from continental European mathematicians for many years, to the detriment of English mathematics.

It is Leibniz, however, who gave the new discipline its name. Newton called his calculus " the science of fluxions ". Since the time of Leibniz and Newton, many mathematicians have contributed to the continuing development of calculus. One of the first and most complete works on both infinitesimal and integral calculus was written in by Maria Gaetana Agnesi.

In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley. Berkeley famously described infinitesimals as the ghosts of departed quantities in his book The Analyst in Working out a rigorous foundation for calculus occupied mathematicians for much of the century following Newton and Leibniz, and is still to some extent an active area of research today.

Several mathematicians, including Maclaurin , tried to prove the soundness of using infinitesimals, but it would not be until years later when, due to the work of Cauchy and Weierstrass , a way was finally found to avoid mere "notions" of infinitely small quantities. Following the work of Weierstrass, it eventually became common to base calculus on limits instead of infinitesimal quantities, though the subject is still occasionally called "infinitesimal calculus".

Bernhard Riemann used these ideas to give a precise definition of the integral. It was also during this period that the ideas of calculus were generalized to Euclidean space and the complex plane. In modern mathematics, the foundations of calculus are included in the field of real analysis , which contains full definitions and proofs of the theorems of calculus.

The reach of calculus has also been greatly extended. Henri Lebesgue invented measure theory and used it to define integrals of all but the most pathological functions. Laurent Schwartz introduced distributions , which can be used to take the derivative of any function whatsoever.By a program, roots are 1. Thus 1 , 0. Basic numeracy skills, such as the ability to tell the time, count money and carry out simple arithmetic , became essential in this new urban lifestyle.

Thus the slope is undefined. The cost of an item as a function of the time of day, x is A. Thus H and J are upper triangular. Ernest F. In early calculus the use of infinitesimal quantities was thought unrigorous, and was fiercely criticized by a number of authors, most notably Michel Rolle and Bishop Berkeley.

The revenue for selling x type A magnets and y type B magnets is 2.

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