# Calculus

## Quarter 2

### Learning Objectives:

• Evaluate an improper integral or determine that the integral diverges.
• Calculate areas in the plane using the definite integral.

### Learning Objectives:

• 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.

### Learning Objectives:

• 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.

### Learning Objectives:

• 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.

### Learning Objectives:

• 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.

### Learning Objectives:

• Calculate derivatives of functions written in polar coordinates.
• Calculate areas of regions defined by polar curves using definite integrals

### Learning Objectives:

• 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.

### Learning Objectives:

• 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.

### Assignments:

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