• Determine the volume of revolution
• Find the volume of a solid using integration (including the method of shells)
• Techniques of integration (Substitution from Chapter 5, and 7.1, 7.2, 7.3, 7.4, 7.5 - see Mastery Test)
• Convergence/Divergence of Improper Integrals by evaluation
• Convergence/Divergence of Improper Integrals by comparison
• Find the work done by a force, including problems on Hooke's Law
• Find the arc length of a curve
• Find the area of a surface of revolution
• Determine the hydrostatic force against a vertical side of a container containing some fluid.
• Given the parametric equations of a curve, be able to find:
• the first and second derivatives of the function in cartesian coordinates
• the equation of a tangent to the curve at some specified point
• points on the curve where the tangent is horizontal/vertical
• arc length of the curve
• area of surface of revolution
• Polar Coordinates - Find the slope of the curve at some point and find points on the curve where the tangent is horizontal
• Find the limit of a sequence
• Determine if a sequence is monotonic, bounded
• Test a sequence for convergence - Squeeze Theorem for sequences, Monotonic Sequence Theorem
• Determine if a series is convergent or divergent and in some cases, be able to find the sum of aconvergent series - includes geometric series, telescoping sum
• Know the n-th term Test for divergence
• Be able to use the Integral Test to determine whether or not a series is convergent.
• Approximate the sum of of a convergent series and estimate the error in the approximation
• Find the number of terms required to ensure the approximation is accurate to within some given positive number of the sum
• The Comparison Test and The Limit Comparison Test
• Alternating Series Test for convergence
• Alternating Series Estimation Theorem
• Determine whether a series is absolutely convergent/conditionally convergent
• Ratio Test and Root Test
• Be able to find the radius of convergence and interval of convergence of a power series
• Representation of functions as power series - Taylor and Maclaurin series
• Evaluate indefinite integrals as infinte series
• Use series to approximate definite integrals to within an indicated accuracy