# Math 129 - Calculus II Worksheets

The following is a list of worksheets and other materials related to Math 129 at the UA. Your instructor might use some of these in class. You may also use any of these materials for practice. The chapter headings refer to Calculus, Sixth Edition by Hughes-Hallett et al. Published by Wiley.

## CHAPTER 7 - Integration

• Derivative and Integral Rules - A compact list of basic rules.   pdf  doc
• Trig Reference Sheet - List of basic identities and rules for trig functions.   pdf   doc
• Recognizing Integrals - Similar looking integrals require different techniques. Determine if algebra or substitution is needed.   pdf   doc
• U-Substitution - Practice with u-substitution, including changing endpoints.   pdf   doc
• More Substitution - Substitution in symbolic form.   pdf   doc
• Trig Substitution & Partial Fraction - These problems cannot be done using the table of integrals in the text.   pdf   doc
• More Trig Sub & Partial Fractions - These problems should be done without the use of a table of integrals.   pdf   doc
• Integral Table - Table of integrals.   pdf
• Complete Square & Division - Algebra review of completion of the square and long division of polynomials.   pdf  doc
• Integration Tables - Manipulate the integrand in order to use a formula in the table of integrals.   pdf   doc
• Integration Techniques - A collection of problems using various integration techniques.   pdf   doc
• Estimation Rules - Illustrating and using the Left, Right, Trapezoid, Midpoint, and Simpson's rules.   pdf   doc
• More Estimation - Another worksheet illustrating the estimation of definite integrals.   pdf   doc
• Intro to Improper Integrals - Introduction to evaluating an improper integral.   pdf   doc
• Improper Integrals - Recognizing an improper integral and using a value of an integral to find other values.   pdf   doc
• Intro to Comparing Improper Integrals - General relationships between functions and the idea behind comparison.   pdf   doc
• Improper Integrals by Comparison - Using comparison to prove an integral converges/ diverges.   pdf   doc
• Improper Integrals by Comparison - Additional practice. Antiderivatives cannot be expressed in closed form.   pdf   doc
• Evaluating Limits - Additional practice. Evaluating limits. L'Hopital's Rule.   pdf   doc

## CHAPTER 8 - Using the Definite Integral

• Intro to Slicing - How slicing can be used to construct a Riemann sum or definite integral.  pdf   doc
• Slicing a Solid - Additional practice. Slicing a solid in two ways to find volume.  pdf
• Geometry - Additional practice. Find area, volume, and length. Includes using density.  pdf   doc
• More Geometry - Additional practice. More applications to geometry.  pdf   doc
• Density and Mass - Using density and slicing to find mass.  pdf   doc
• Physics - Additional practice. Problems involve work.  pdf   doc
• More Work - Additional practice. More problems involving work.  pdf   doc

## CHAPTER 9 - Sequences and Series

• Geometric Series - Additional practice with geometric series.  pdf   doc
• Integral Test - Using the integral test to determine if series converge.  pdf   doc
• Convergence Tests - Additional practice using convergence tests.  pdf   doc
• More Convergence Tests - A summary of the available convergence tests.  pdf   doc
• Power Series - Working with power series.  pdf   doc
• More Power Series - Additional practice finding radius and interval of convergence.  pdf   doc

## CHAPTER 10 - Approximating Functions Using Series

• Taylor Polynomials & series - How well do Taylor polynomials approximate functions values?  pdf   doc
• Series Table - List of Taylor Series for basic functions.   pdf
• Using Taylor Series - Different ways to use Taylor series.  pdf   doc
• Taylor Series - Additional practice.  pdf   doc
• More Taylor Series - Collection of problems using Taylor series.  pdf   doc
• More Taylor Series - Additional practice.  pdf   doc
• Complex Numbers - Algebra of complex numbers and Euler's Form.   pdf   doc

## CHAPTER 11 - Differential Equations

• Slopefields - Matching slopefields with differential equations.  pdf
• Separable Variables - Using the method of separation of variables to solve differential equations.  pdf   doc
• Differential Equations - Collection of applications.  pdf   doc
• Models - Comparing various models including Logistic.  pdf   doc