, INSTRUCTOR’S
SOLUTIONS MANUAL
DUANE KOUBA
University of California, Davis
T HOMAS ’ C ALCULUS
E ARLY T RANSCENDENTALS
FOURTEENTH EDITION
Based on the original work by
George B. Thomas, Jr
Massachusetts Institute of Technology
as revised by
Joel Hass
University of California, Davis
Christopher Heil
Georgia Institute of Technology
Maurice D. Weir
Naval Postgraduate School
,The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher
make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this
book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with,
or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2018, 2014, 2010 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
publisher. Printed in the United States of America.
ISBN-13: 978-0-13-443932-7
ISBN-10: 0-13-443932-5
, TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 9
1.3 Trigonometric Functions 19
1.4 Graphing with Software 27
1.5 Exponential Functions 32
1.6 Inverse Functions and Logarithms 35
Practice Exercises 45
Additional and Advanced Exercises 55
2 Limits and Continuity 61
2.1 Rates of Change and Tangents to Curves 61
2.2 Limit of a Function and Limit Laws 65
2.3 The Precise Definition of a Limit 75
2.4 One-Sided Limits 83
2.5 Continuity 88
2.6 Limits Involving Infinity; Asymptotes of Graphs 94
Practice Exercises 105
Additional and Advanced Exercises 111
3 Derivatives 119
3.1 Tangents and the Derivative at a Point 119
3.2 The Derivative as a Function 125
3.3 Differentiation Rules 136
3.4 The Derivative as a Rate of Change 142
3.5 Derivatives of Trigonometric Functions 148
3.6 The Chain Rule 157
3.7 Implicit Differentiation 168
3.8 Derivatives of Inverse Functions and Logarithms 176
3.9 Inverse Trigonometric Functions 186
3.10 Related Rates 193
3.11 Linearization and Differentials 198
Practice Exercises 206
Additional and Advanced Exercises 220
Copyright 2018 Pearson Education, Inc.
iii
SOLUTIONS MANUAL
DUANE KOUBA
University of California, Davis
T HOMAS ’ C ALCULUS
E ARLY T RANSCENDENTALS
FOURTEENTH EDITION
Based on the original work by
George B. Thomas, Jr
Massachusetts Institute of Technology
as revised by
Joel Hass
University of California, Davis
Christopher Heil
Georgia Institute of Technology
Maurice D. Weir
Naval Postgraduate School
,The author and publisher of this book have used their best efforts in preparing this book. These efforts include the
development, research, and testing of the theories and programs to determine their effectiveness. The author and publisher
make no warranty of any kind, expressed or implied, with regard to these programs or the documentation contained in this
book. The author and publisher shall not be liable in any event for incidental or consequential damages in connection with,
or arising out of, the furnishing, performance, or use of these programs.
Reproduced by Pearson from electronic files supplied by the author.
Copyright © 2018, 2014, 2010 Pearson Education, Inc.
Publishing as Pearson, 330 Hudson Street, NY NY 10013
All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form
or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the
publisher. Printed in the United States of America.
ISBN-13: 978-0-13-443932-7
ISBN-10: 0-13-443932-5
, TABLE OF CONTENTS
1 Functions 1
1.1 Functions and Their Graphs 1
1.2 Combining Functions; Shifting and Scaling Graphs 9
1.3 Trigonometric Functions 19
1.4 Graphing with Software 27
1.5 Exponential Functions 32
1.6 Inverse Functions and Logarithms 35
Practice Exercises 45
Additional and Advanced Exercises 55
2 Limits and Continuity 61
2.1 Rates of Change and Tangents to Curves 61
2.2 Limit of a Function and Limit Laws 65
2.3 The Precise Definition of a Limit 75
2.4 One-Sided Limits 83
2.5 Continuity 88
2.6 Limits Involving Infinity; Asymptotes of Graphs 94
Practice Exercises 105
Additional and Advanced Exercises 111
3 Derivatives 119
3.1 Tangents and the Derivative at a Point 119
3.2 The Derivative as a Function 125
3.3 Differentiation Rules 136
3.4 The Derivative as a Rate of Change 142
3.5 Derivatives of Trigonometric Functions 148
3.6 The Chain Rule 157
3.7 Implicit Differentiation 168
3.8 Derivatives of Inverse Functions and Logarithms 176
3.9 Inverse Trigonometric Functions 186
3.10 Related Rates 193
3.11 Linearization and Differentials 198
Practice Exercises 206
Additional and Advanced Exercises 220
Copyright 2018 Pearson Education, Inc.
iii
