- Evaluate an improper integral or determine that the integral diverges.
- Calculate areas in the plane using the definite integral.
- Calculate volumes of solids with known cross sections using definite integrals.
- Calculate volumes of solids of revolution using definite integrals.
- Determine the length of a curve in the plane defined by a function, using a definite integral.
- Interpret differential equations via slope fields and show the relationship between slope fields and solution curves.
- Find numerical solutions to differential equations using Euler's method.
- Sketch solution curves to logistic differential equations.
- Determine the intervals where a logistic differential equation's solution is increasing or decreasing.
- Solve simple logistic differential equations and use them to model population growth and decay.
- Calculate derivatives of parametric functions.
- Determine the length of a curve in the plane defined by parametric functions, using a definite integral.
- Calculate derivatives of vector valued functions.
- Determine a particular solution given a rate vector and initial conditions.
- Determine values for positions and rates of change in problems involving planar motion.
- Calculate derivatives of functions written in polar coordinates.
- Calculate areas of regions defined by polar curves using definite integrals
- Show convergence of sequences including decimal expansions.
- Show convergence or divergence of geometric series.
- Show the divergence of the harmonic series.
- Show convergence of p-series using the integral test.
- Show convergence of series using the comparison tests.
- Show the interval of convergence of series using the ratio test.
- Identify a series' radius of convergence.
- Show the convergence of series using the alternating series test (including the alternating harmonic series).
- Determine the intervals where a series converges absolutely and conditionally.
- Use the ratio test (or root test) to find a power series interval of convergence.
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