Student Solutions Manual for Calculus

<table> <tbody> <tr> <td> <p style="margin: 0px;">0 PRELIMINARIES</p> <p style="margin: 0px;">0.1 Real Numbers, Logic and Estimation</p> <p style="margin: 0px;">0.2 Inequalities and Absolute Values</p> <p style="margin: 0px;">0.3 The Rectangular Coordinate System</p> <p style="margin: 0px;">0.4 Graphs of Equations</p> <p style="margin: 0px;">0.5 Functions and Their Graphs</p> <p style="margin: 0px;">0.6 Operations on Functions</p> <p style="margin: 0px;">0.7 The Trigonometric Functions</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">1 LIMITS</p> <p style="margin: 0px;">1.1 Introduction to Limits</p> <p style="margin: 0px;">1.2 Rigorous Study of Limits</p> <p style="margin: 0px;">1.3 Limit Theorems</p> <p style="margin: 0px;">1.4 Limits Involving Trigonometric Functions</p> <p style="margin: 0px;">1.5 Limits at Infinity, Infinite Limits</p> <p style="margin: 0px;">1.6 Continuity of Functions</p> <p style="margin: 0px;">1.7 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">2 THE DERIVATIVE</p> <p style="margin: 0px;">2.1 Two Problems with One Theme</p> <p style="margin: 0px;">2.2 The Derivative</p> <p style="margin: 0px;">2.3 Rules for Finding Derivatives</p> <p style="margin: 0px;">2.4 Derivatives of Trigonometric Functions</p> <p style="margin: 0px;">2.5 The Chain Rule</p> <p style="margin: 0px;">2.6 Higher-Order Derivatives</p> <p style="margin: 0px;">2.7 Implicit Differentiation</p> <p style="margin: 0px;">2.8 Related Rates</p> <p style="margin: 0px;">2.9 Differentials and Approximations</p> <p style="margin: 0px;">2.10 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">3 APPLICATIONS OF THE DERIVATIVE</p> <p style="margin: 0px;">3.1 Maxima and Minima</p> <p style="margin: 0px;">3.2 Monotonicity and Concavity</p> <p style="margin: 0px;">3.3 Local Extrema and Extrema on Open Intervals</p> <p style="margin: 0px;">3.4 Graphing Functions Using Calculus</p> <p style="margin: 0px;">3.6 The Mean Value Theorem for Derivatives</p> <p style="margin: 0px;">3.7 Solving Equations Numerically</p> <p style="margin: 0px;">3.8 Antiderivatives</p> <p style="margin: 0px;">3.9 Introduction to Differential Equations</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">4 THE DEFINITE INTEGRAL</p> <p style="margin: 0px;">4.1 Introduction to Area</p> <p style="margin: 0px;">4.2 The Definite Integral</p> <p style="margin: 0px;">4.3 The 1st Fundamental Theorem of Calculus</p> <p style="margin: 0px;">4.4 The 2nd Fundamental Theorem of Calculus</p> <p style="margin: 0px;">and the Method of Substitution</p> <p style="margin: 0px;">4.5 The Mean Value Theorem for Integrals &amp; the Use of Symmetry</p> <p style="margin: 0px;">4.6 Numerical Integration</p> <p style="margin: 0px;">4.7 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">5 APPLICATIONS OF THE INTEGRAL</p> <p style="margin: 0px;">5.1 The Area of a Plane Region</p> <p style="margin: 0px;">5.2 Volumes of Solids: Slabs, Disks, Washers</p> <p style="margin: 0px;">5.3 Volumes of Solids of Revolution: Shells</p> <p style="margin: 0px;">5.4 Length of a Plane Curve</p> <p style="margin: 0px;">5.5 Work and Fluid Pressure</p> <p style="margin: 0px;">5.6 Moments, Center of Mass</p> <p style="margin: 0px;">5.7 Probability and Random Variables</p> <p style="margin: 0px;">5.8 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">6 TRANSCENDENTAL FUNCTIONS</p> <p style="margin: 0px;">6.1 The Natural Logarithm Function</p> <p style="margin: 0px;">6.2 Inverse Functions and Their Derivatives</p> <p style="margin: 0px;">6.3 The Natural Exponential Function</p> <p style="margin: 0px;">6.4 General Exponential &amp; Logarithmic Functions</p> <p style="margin: 0px;">6.5 Exponential Growth and Decay</p> <p style="margin: 0px;">6.6 First-Order Linear Differential Equations</p> <p style="margin: 0px;">6.7 Approximations for Differential Equations</p> <p style="margin: 0px;">6.8 Inverse Trig Functions &amp; Their Derivatives</p> <p style="margin: 0px;">6.9 The Hyperbolic Functions &amp; Their Inverses</p> <p style="margin: 0px;">6.10 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">7 TECHNIQUES OF INTEGRATION</p> <p style="margin: 0px;">7.1 Basic Integration Rules</p> <p style="margin: 0px;">7.2 Integration by Parts</p> <p style="margin: 0px;">7.3 Some Trigonometric Integrals</p> <p style="margin: 0px;">7.4 Rationalizing Substitutions</p> <p style="margin: 0px;">7.5 The Method of Partial Fractions</p> <p style="margin: 0px;">7.6 Strategies for Integration</p> <p style="margin: 0px;">7.7 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">8 INDETERMINATE FORMS &amp;&nbsp;IMPROPER INTEGRALS</p> <p style="margin: 0px;">8.1 Indeterminate Forms of Type 0/0</p> <p style="margin: 0px;">8.2 Other Indeterminate Forms</p> <p style="margin: 0px;">8.3 Improper Integrals: Infinite Limits of Integration</p> <p style="margin: 0px;">8.4 Improper Integrals: Infinite Integrands</p> <p style="margin: 0px;">8.5 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">9 INFINITE SERIES</p> <p style="margin: 0px;">9.1 Infinite Sequences</p> <p style="margin: 0px;">9.2 Infinite Series</p> <p style="margin: 0px;">9.3 Positive Series: The Integral Test</p> <p style="margin: 0px;">9.4 Positive Series: Other Tests</p> <p style="margin: 0px;">9.5 Alternating Series, Absolute Convergence,</p> <p style="margin: 0px;">and Conditional Convergence</p> <p style="margin: 0px;">9.6 Power Series</p> <p style="margin: 0px;">9.7 Operations on Power Series</p> <p style="margin: 0px;">9.8 Taylor and Maclaurin Series</p> <p style="margin: 0px;">9.9 The Taylor Approximation to a Function</p> <p style="margin: 0px;">9.10 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">10 CONICS AND POLAR COORDINATES</p> <p style="margin: 0px;">10.1 The Parabola</p> <p style="margin: 0px;">10.2 Ellipses and Hyperbolas</p> <p style="margin: 0px;">10.3 Translation and Rotation of Axes</p> <p style="margin: 0px;">10.4 Parametric Representation of Curves</p> <p style="margin: 0px;">10.5 The Polar Coordinate System</p> <p style="margin: 0px;">10.6 Graphs of Polar Equations</p> <p style="margin: 0px;">10.7 Calculus in Polar Coordinates</p> <p style="margin: 0px;">10.8 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">11 GEOMETRY IN SPACE, VECTORS</p> <p style="margin: 0px;">11.1 Cartesian Coordinates in Three-Space</p> <p style="margin: 0px;">11.2 Vectors</p> <p style="margin: 0px;">11.3 The Dot Product</p> <p style="margin: 0px;">11.4 The Cross Product</p> <p style="margin: 0px;">11.5 Vector Valued Functions &amp; Curvilinear Motion</p> <p style="margin: 0px;">11.6 Lines in Three-Space</p> <p style="margin: 0px;">11.7 Curvature and Components of Acceleration</p> <p style="margin: 0px;">11.8 Surfaces in Three Space</p> <p style="margin: 0px;">11.9 Cylindrical and Spherical Coordinates</p> <p style="margin: 0px;">11.10 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">12 DERIVATIVES OF FUNCTIONS OF TWO OR MORE VARIABLES</p> <p style="margin: 0px;">12.1 Functions of Two or More Variables</p> <p style="margin: 0px;">12.2 Partial Derivatives</p> <p style="margin: 0px;">12.3 Limits and Continuity</p> <p style="margin: 0px;">12.4 Differentiability</p> <p style="margin: 0px;">12.5 Directional Derivatives and Gradients</p> <p style="margin: 0px;">12.6 The Chain Rule</p> <p style="margin: 0px;">12.7 Tangent Planes, Approximations</p> <p style="margin: 0px;">12.8 Maxima and Minima</p> <p style="margin: 0px;">12.9 Lagrange Multipliers</p> <p style="margin: 0px;">12.10 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">13 MULTIPLE INTEGRATION</p> <p style="margin: 0px;">13.1 Double Integrals over Rectangles</p> <p style="margin: 0px;">13.2 Iterated Integrals</p> <p style="margin: 0px;">13.3 Double Integrals over Nonrectangular Regions</p> <p style="margin: 0px;">13.4 Double Integrals in Polar Coordinates</p> <p style="margin: 0px;">13.5 Applications of Double Integrals</p> <p style="margin: 0px;">13.6 Surface Area</p> <p style="margin: 0px;">13.7 Triple Integrals (Cartesian Coordinates)</p> <p style="margin: 0px;">13.8 Triple Integrals (Cyl &amp; Sph Coordinates)</p> <p style="margin: 0px;">13.9 Change of Variables in Multiple Integrals</p> <p style="margin: 0px;">13.1 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">14 VECTOR CALCULUS</p> <p style="margin: 0px;">14.1 Vector Fields</p> <p style="margin: 0px;">14.2 Line Integrals</p> <p style="margin: 0px;">14.3 Independence of Path</p> <p style="margin: 0px;">14.4 Green's Theorem in the Plane</p> <p style="margin: 0px;">14.5 Surface Integrals</p> <p style="margin: 0px;">14.6 Gauss's Divergence Theorem</p> <p style="margin: 0px;">14.7 Stokes's Theorem</p> <p style="margin: 0px;">14.8 Chapter Review</p> <p style="margin: 0px;">&nbsp;</p> <p style="margin: 0px;">APPENDIX</p> <p style="margin: 0px;">A.1 Mathematical Induction</p> <p style="margin: 0px;">A.2 Proofs of Several Theorems</p> <p style="margin: 0px;">A.3 A Backward Look</p></td> <td> <p style="margin: 0px;">&nbsp;</p></td> </tr> </tbody> </table>