### Solution Manual for Single Variable Calculus Early Transcendentals 2nd Edition by William L. Briggs

#### Solution Manual for Single Variable Calculus Early Transcendentals 2nd Edition by William L. Briggs

**For a three-semester or four-quarter calculus course covering single variable and multivariable calculus for mathematics, engineering, and science majors.**

This much anticipated second edition of the most successful new calculus text published in the last two decades retains the best of the first edition while introducing important advances and refinements. Authors Briggs, Cochran, and Gillett build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor, examples that are stepped out and thoughtfully annotated, and figures that are designed to teach rather than simply supplement the narrative. The authors appeal to students’ geometric intuition to introduce fundamental concepts, laying a foundation for the development that follows. The groundbreaking eBook contains over 650 Interactive Figures that can be manipulated to shed light on key concepts.

This text offers a superior teaching and learning experience. Here’s how:

**A robust MyMathLab**^{®}**course**contains more than 7,000 assignable exercises, an eBook with 650 Interactive Figures, and built-in tutorials so students can get help when they need it.**Reflects how students use a textbook**–they start with the exercises and flip back for help if they need it.**Organization and presentation of content facilitates learning**of key concepts, skills, and applications.

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## Table of Contents

**1. Functions**

1.1 Review of functions

1.2 Representing functions

1.3 Inverse, exponential, and logarithmic functions

1.4 Trigonometric functions and their inverses

**2. Limits**

2.1 The idea of limits

2.2 Definitions of limits

2.3 Techniques for computing limits

2.4 Infinite limits

2.5 Limits at infinity

2.6 Continuity

2.7 Precise definitions of limits

**3. Derivatives**

3.1 Introducing the derivative

3.2 Working with derivatives

3.3 Rules of differentiation

3.4 The product and quotient rules

3.5 Derivatives of trigonometric functions

3.6 Derivatives as rates of change

3.7 The Chain Rule

3.8 Implicit differentiation

3.9 Derivatives of logarithmic and exponential functions

3.10 Derivatives of inverse trigonometric functions

3.11 Related rates

**4. Applications of the Derivative**

4.1 Maxima and minima

4.2 What derivatives tell us

4.3 Graphing functions

4.4 Optimization problems

4.5 Linear approximation and differentials

4.6 Mean Value Theorem

4.7 L’Hôpital’s Rule

4.8 Newton’s Method

4.9 Antiderivatives

**5. Integration**

5.1 Approximating areas under curves

5.2 Definite integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with integrals

5.5 Substitution rule

**6. Applications of Integration**

6.1 Velocity and net change

6.2 Regions between curves

6.3 Volume by slicing

6.4 Volume by shells

6.5 Length of curves

6.6 Surface area

6.7 Physical applications

6.8 Logarithmic and exponential functions revisited

6.9 Exponential models

6.10 Hyperbolic functions

**7. Integration Techniques**

7.1 Basic approaches

7.2 Integration by parts

7.3 Trigonometric integrals

7.4 Trigonometric substitutions

7.5 Partial fractions

7.6 Other integration strategies

7.7 Numerical integration

7.8 Improper integrals

7.9 Introduction to differential equations

**8. Sequences and Infinite Series**

8.1 An overview

8.2 Sequences

8.3 Infinite series

8.4 The Divergence and Integral Tests

8.5 The Ratio, Root, and Comparison Tests

8.6 Alternating series

**9. Power Series**

9.1 Approximating functions with polynomials

9.2 Properties of Power series

9.3 Taylor series

9.4 Working with Taylor series

**10. Parametric and Polar Curves**

10.1 Parametric equations

10.2 Polar coordinates

10.3 Calculus in polar coordinates

10.4 Conic sections

**11. Vectors and Vector-Valued Functions**

11.1 Vectors in the plane

11.2 Vectors in three dimensions

11.3 Dot products

11.4 Cross products

11.5 Lines and curves in space

11.6 Calculus of vector-valued functions

11.7 Motion in space

11.8 Length of curves

11.9 Curvature and normal vectors

**12. Functions of Several Variables**

12.1 Planes and surfaces

12.2 Graphs and level curves

12.3 Limits and continuity

12.4 Partial derivatives

12.5 The Chain Rule

12.6 Directional derivatives and the gradient

12.7 Tangent planes and linear approximation

12.8 Maximum/minimum problems

12.9 Lagrange multipliers

**13. Multiple Integration**

13.1 Double integrals over rectangular regions

13.2 Double integrals over general regions

13.3 Double integrals in polar coordinates

13.4 Triple integrals

13.5 Triple integrals in cylindrical and spherical coordinates

13.6 Integrals for mass calculations

13.7 Change of variables in multiple integrals

**14. Vector Calculus**

14.1 Vector fields

14.2 Line integrals

14.3 Conservative vector fields

14.4 Green’s theorem

14.5 Divergence and curl

14.6 Surface integrals

14.6 Stokes’ theorem

14.8 Divergence theorem

Appendix A. Algebra Review

Appendix B. Proofs of Selected Theorems

**D1. Differential Equations (online)**

D1.1 Basic Ideas

D1.2 Direction Fields and Euler’s Method

D1.3 Separable Differential Equations

D1.4 Special First-Order Differential Equations

D1.5 Modeling with Differential Equations

**D2. Second-Order Differential Equations (online)**

D2.1 Basic Ideas

D2.2 Linear Homogeneous Equations

D2.3 Linear Nonhomogeneous Equations

D2.4 Applications

##### D2.5 Complex Forcing Functions

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#### Solution Manual for Single Variable Calculus Early Transcendentals 2nd Edition by William L. Briggs