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Each Solved Problem book helps you cut study time, hone problem-solving skills, and achieve your personal best on exams! You get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Solved Problems gives you 3, solved problems covering every area of calculus Step-by-step approach to problems Hundreds of clear diagrams and illustrations Fully compatible with your classroom text, Schaum's highlights all the problem-solving skills you need to know.

Use Schaum's to shorten your study time, increase your test scores, and get your best possible final grade. Schaum's Outlines--Problem Solved. This powerful problem-solver gives you 3, problems in calculus, fully solved step-by-step! Work the problems yourself, then check the answers, or go directly to the answers you need with a complete index.

Tough Test Questions? Fortunately, there's Schaum's. This all-in-one-package includes more than 1, fully solved problems, examples, and practice exercises to sharpen your problem-solving skills. Plus, you will have access to 30 detailed videos featuring Math instructors who explain how to solve the most commonly tested problems--it's just like having your own virtual tutor!

Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills. This Schaum's Outline gives you 1, fully solved problems Concise explanations of all calculus concepts Expert tips on using the graphing calculator Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time--and get your best test scores!

Ideal for self-instruction as well as for classroom use, this text improves understanding and problem-solving skills in analysis, analytic geometry, and higher algebra. Over 1, problems, with hints and complete solutions. Master physics with Schaum's--the high-performance solved-problem guide.

It will help you cut study time, hone problem-solving skills, and achieve your personal best on exams! Students love Schaum's Solved Problem Guides because they produce results. Determine k so that the points A 7,5 , B -l, 2 , and C k, 0 are the vertices of a right triangle with right angle at B. Find the slope-intercept equation of the line through 1,4 and rising 5 units for each unit increase in x. Since the line rises 5 units for each unit increase in x, its slope must be 5.

Use slopes to show that the points A 5, 4 , B -4, 2 , C -3, -3 , and D 6,-1 are vertices of a parallelogram. Thus, ABCD is a parallelogram. By the solution to Problem 3.

By solving for y, the slope of 2x 3y 1 is found to be. For perpendicularity, the product of the slopes must be 1. Find the midpoint of the line segment between 2, 5 and 1, 3. By the midpoint formula, the coordinates of the midpoint are the averages of the coordinates of the endpoints. A triangle has vertices A l,2 , B 8,1 , C 2,3.

Find the equation of the median from A to the midpoint M of the opposite side. For the triangle of Problem 3. Hence, the slope of the altitude is the negative reciprocal of 1, namely, 1. So, The slope of AB is 2-! Hence, the slope of the desired line is the negative reciprocal of -7, that is, 7. Case 1. As in the solution of Problem 3. Case 2. Then a procedure similar to that in the solution of Problem 3. Refer to Fig. Let Cbe c, e and let D be d, f. Thus, M1M2M3M4 is a parallelogram.

Note two special cases. Then B is -a, 0. Nowthe distance formula gives as required. Find the intersection of the line L through 1, 2 and 5, 8 with the line M through 2,2 and 4, 0. Find equations ofthelines ofslope that form with the coordinate axes a triangle ofarea 24 square units.

So, thex-intercept a is Find an equation of the path of the point. Find the equations of the lines through 4, 2 and at a perpendicular distance of 2 units from the origin.

In Problems 3. Through the points -2,3 and 4,8. Having slope 2 and y-intercept 1. Through 1,4 and parallel to the x-axis. Since the line is parallel to the jc-axis, the line is horizontal. LINES 15 3. Through 1, -4 and rising 5 units for each unit increase in x. Its slope must be 5. Through 5,1 and falling 3 units for each unit increase in x. Its slope must be So, the slope of L is 3. Hence, our line has slope 3.

Through 4,3 and perpendicular to the line with the equation x l. So, our line is horizontal. Its points are equidistant from the positive x- and y-axes.

So, 1,1 is on the line, and its slope is 1. So, 1,9 is on the line. Hence, 4,5 is on the line. So, 1,-2 lies on the line. Another point is 1,2. So, 3, 0 is on the line. Since the lines both have slope 5, they are parallel. Since the slopes of the lines are 1 and 2, the lines are neither parallel nor perpendicular. LINES 3. Hence, the lines are parallel.

The slope of the first line is2 and the slope of the second line is -. Since the product of the slopes is 1,the lines are perpendicular. The slope of thefirstline is -1and the slope ofthesecond line is - j.

Since theslopes are notequal and their product is not 1, the lines are neither parallel nor perpendicular. Temperature is usually measured either in Fahrenheit or in Celsius degrees. The relation between Fahrenheit and Celsius temperatures is given by a linear equation.

Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise. To the Student This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus.

We have aimed at presenting the broadest range of problems that you are likely to encounterthe old chestnuts, all the current standard types, and some not so standard.

Each chapter begins with very elementary problems. Their difficulty usually increases as the chapter pro- gresses, but there is no uniform pattern. It is assumed that you have available a calculus textbook, including tables for the trigonometric, logarith- mic, and exponential functions. Our ordering of the chapters follows the customary order found in many textbooks, but as no two textbooks have exactly the same sequence of topics, you must expect an occasional discrepancy from the order followed in your course.

The printed solution that immediately follows a problem statement gives you all the details of one way to solve the problem. You might wish to delay consulting that solution until you have outlined an attack in your own mind.

You might even disdain to read it until, with pencil and paper, you have solved the problem yourself or failed gloriously. Used thus, Solved Problems in Calculus can almost serve as a supple- ment to any course in calculus, or even as an independent refresher course.

This page intentionally left blank 7. Then, by Problem 3. Conversely, assume M is parallel to L. Hence, by Problem 3. LINES 11 3. Hence, the slope of M is the negative reciprocal BIA; its and thence towhich is equivalent to Use slopes to determine whether the points A 4,1 , 5 7, 3 , and C 3,9 are the vertices of a right triangle.

Determine k so that the points A 7,5 , B -l, 2 , and C k, 0 are the vertices of a right triangle with right angle at B. Find the slope-intercept equation of the line through 1,4 and rising 5 units for each unit increase in x.

Since the line rises 5 units for each unit increase in x, its slope must be 5. Use slopes to show that the points A 5, 4 , B -4, 2 , C -3, -3 , and D 6,-1 are vertices of a parallelogram.

Thus, ABCD is a parallelogram. By the solution to Problem 3. By solving for y, the slope of 2x 3y 1 is found to be.

For perpendicularity, the product of the slopes must be 1. Find the midpoint of the line segment between 2, 5 and 1, 3. By the midpoint formula, the coordinates of the midpoint are the averages of the coordinates of the endpoints. A triangle has vertices A l,2 , B 8,1 , C 2,3.

Find the equation of the median from A to the midpoint M of the opposite side. For the triangle of Problem 3.

Hence, the slope of the altitude is the negative reciprocal of 1, namely, 1. So, The slope of AB is 2-! Hence, the slope of the desired line is the negative reciprocal of -7, that is, 7. Case 1. As in the solution of Problem 3. Case 2. Then a procedure similar to that in the solution of Problem 3. Refer to Fig. Let Cbe c, e and let D be d, f. Thus, M1M2M3M4 is a parallelogram.

Note two special cases. Then B is -a, 0. Nowthe distance formula gives as required. Find the intersection of the line L through 1, 2 and 5, 8 with the line M through 2,2 and 4, 0. Find equations ofthelines ofslope that form with the coordinate axes a triangle ofarea 24 square units. So, thex-intercept a is Find an equation of the path of the point. Find the equations of the lines through 4, 2 and at a perpendicular distance of 2 units from the origin. In Problems 3. Through the points -2,3 and 4,8.

Having slope 2 and y-intercept 1. Through 1,4 and parallel to the x-axis. Since the line is parallel to the jc-axis, the line is horizontal. LINES 15 3. Through 1, -4 and rising 5 units for each unit increase in x. Its slope must be 5. Through 5,1 and falling 3 units for each unit increase in x. Its slope must be All rights reserved.

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Neither McGraw-Hill nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill has no responsibility for the content of any information accessed through the work. This limitation of liability shall apply to any claim or cause whatsoever whether such claim or cause arises in contract, tort or otherwise.

To the Student This collection of solved problems covers elementary and intermediate calculus, and much of advanced calculus. We have aimed at presenting the broadest range of problems that you are likely to encounterthe old chestnuts, all the current standard types, and some not so standard. Each chapter begins with very elementary problems. Their difficulty usually increases as the chapter pro- gresses, but there is no uniform pattern. It is assumed that you have available a calculus textbook, including tables for the trigonometric, logarith- mic, and exponential functions.

Our ordering of the chapters follows the customary order found in many textbooks, but as no two textbooks have exactly the same sequence of topics, you must expect an occasional discrepancy from the order followed in your course.

The printed solution that immediately follows a problem statement gives you all the details of one way to solve the problem. You might wish to delay consulting that solution until you have outlined an attack in your own mind.

You might even disdain to read it until, with pencil and paper, you have solved the problem yourself or failed gloriously. Used thus, Solved Problems in Calculus can almost serve as a supple- ment to any course in calculus, or even as an independent refresher course. This page intentionally left blank 7.

Then, by Problem 3. Conversely, assume M is parallel to L. Hence, by Problem 3. LINES 11 3. Hence, the slope of M is the negative reciprocal BIA; its and thence towhich is equivalent to Use slopes to determine whether the points A 4,1 , 5 7, 3 , and C 3,9 are the vertices of a right triangle. Determine k so that the points A 7,5 , B -l, 2 , and C k, 0 are the vertices of a right triangle with right angle at B.

Find the slope-intercept equation of the line through 1,4 and rising 5 units for each unit increase in x. Since the line rises 5 units for each unit increase in x, its slope must be 5. Use slopes to show that the points A 5, 4 , B -4, 2 , C -3, -3 , and D 6,-1 are vertices of a parallelogram. Thus, ABCD is a parallelogram. By the solution to Problem 3. By solving for y, the slope of 2x 3y 1 is found to be. For perpendicularity, the product of the slopes must be 1.

Find the midpoint of the line segment between 2, 5 and 1, 3. By the midpoint formula, the coordinates of the midpoint are the averages of the coordinates of the endpoints. A triangle has vertices A l,2 , B 8,1 , C 2,3. Find the equation of the median from A to the midpoint M of the opposite side.

For the triangle of Problem 3. Hence, the slope of the altitude is the negative reciprocal of 1, namely, 1. So, The slope of AB is 2-! Hence, the slope of the desired line is the negative reciprocal of -7, that is, 7.

Case 1. As in the solution of Problem 3. Case 2. Then a procedure similar to that in the solution of Problem 3. Refer to Fig. Let Cbe c, e and let D be d, f.

Thus, M1M2M3M4 is a parallelogram. Note two special cases. Then B is -a, 0. Nowthe distance formula gives as required. Find the intersection of the line L through 1, 2 and 5, 8 with the line M through 2,2 and 4, 0.

Find equations ofthelines ofslope that form with the coordinate axes a triangle ofarea 24 square units. So, thex-intercept a is Find an equation of the path of the point.

WebSep 16, · Download Solved Problems in Physics Book in PDF, Epub and Kindle Sample problems cover equilibrium, Newton's laws of motion, work, momentum, . WebRead & Download PDF Solved Problems in Calculus, Update the latest version with high-quality. Try NOW! Editor's Picks; Explore; Contact; ?. Table Of Content. . WebSchaum's 3, Solved Problems in Calculus SCHAUM'S OUTLINE OF SOLVED PROBLEMS IN Calculus Elliot Mendelson, Ph.D. Professor of Mathematics Queens .