• Distinguish between determinate and indeterminate forms of limits.
• Use L'Hopital's rule to calculate limits of the proper form.
• Manipulate a limit with indeterminate form so that L'Hopital's rule applies.
• Find limits (whether you need L'Hopital's rule or not!).

Extra Credit(2): In problem 49, find an example of a non-differentiable function where the indicated limit exists.

• Distinguish proper vs. improper integrals.
• Evaluate improper integrals using the fundamental theorem of calculus.
• Use the comparison test to determine if an improper integral converges or diverges.
• Bound a tail of an improper integral, and evaluate it numerically.

• Find the general term of a sequence.
• Learn to reindex a sequence.
• Find the limit of a sequence.
• Determine when a sequence is bounded.
• Determine when a sequence is monotonic.
• Learn the bounded monotononic sequence theorem.

• Tell when a series is convergent or divergent.
• Recognize and sum any geometric series.
• Recognize the harmonic series and know that it diverges.
• Be able to use the nth term test for divergence.
• Sum a telescoping series.

• Apply the comparison test.
• Apply the limit comparison test.
• Apply the integral test.
• Estimate the sum of a series given an error bound.

• Identify Alternating series.
• Apply the alternating series test.
• Distinguish between Convergence and Absolute Convergence.
• Use the Ratio test to determine convergence or divergence of a series.
• Estimate the sum of a series that converges by the ratio test.

• Identify the center of a power series
• Find the radius of a power series.
• Find the interval of convergence of a power series.
• Estimate values of functions given as power series.

• Integrate any power series
• Differentiate any power series
• Find power series related to 1/(1-x) by differentiation, integration, and composition.

• Find a Taylor series for a function
• Use known Taylor series of exp(x), sin(x), cos(x) to find related series.
• Compute binomial coefficients for non-integer powers.
• Compute the binomial series for a (1+x)^k and related series.

• Approximate a function with Taylor Polynomials.
• Estimate the error in a Taylor polynomial approximation.

• Graph parametric equations
• Write parametric equations of circles, ellipses, and lines
• Write parametric equations of functions

• The derivative of a parametric curve
• The area under a parametric curve representing a function
• The arc length of a parametric curve

• Definition of Polar Coordinates, pole, polar axis
• Why polar coordinates are not unique
• When is a point on a polar graph
• How to graph a polar coordinate graph on your calculator
• How to write polar coordinate equations of
  • Circles centered at the origin
  • Circles through the origin
  • Cardioids
  • Limacons
  • Roses
• How to convert between Polar and Rectangular coordinates
• The slope of the tangent line to a polar graph (dy/dx)

• Distinguish between dr/dt, dy/dt, dx/dt, dy/dx
• (H.2) How to set up an integral for the area in polar coordinates
• How to set up an integral for the arc length in polar coordinates

• The general equations of the ellipse, parabola, and hyperbola in Cartesian coordinates.
• How to write an equation for a conic section in polar coordinates
• Given a polar equation, identify the eccentricity
• Given a polar equation, identify the type of conic section