Final Exam Topics:

Chapter 8 (Sections 8.1-8.4): Integration (integration by parts, trigonometric functions, special substitutions)

Chapter 9: Equation of the tangent line to a parametric curve, arc length and speed. Length and area in polar coordinates.

Chapter 10: Sequences: convergence, operation with limits, computing limits with L’Hopital. Special limits. Improper Integrals.

Chapter 11: Series.

• Definitions: main term, partial sums, sum of a series, convergent/divergent series.
• Basic Divergence Test
• Positive series: convergence tests (integral, comparison (basic and limit), root, ratio)
• Non-positive series: absolute convergence, conditional convergence, alternating series test.

Chapter 11.5-11.6: Taylor series and Taylor Polynomials.

Chapter 11.7-11.8: Power series (radius of convergence) and Differentiation and Integration of Power series (Abel’s Theorem).